BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Perimeter calculation

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 131
Joined: Fri Jun 18, 2010 10:19 am
Location: New York, NY
Thanked: 10 times

by aleph777 » Tue Jan 11, 2011 12:00 pm
Hi Steven,

We're given three segments already, so we just need to solve for segments AE and ED.

The clue here is in the 30-degree angles we're given. Imagine that AED were a triangle, and then locate the angle of DAE based on the fact that DAB is 90 degrees and BAE is 30. 90 - 30 = 60. And the same goes for angle ADE. Which makes this an equilateral triangle.

Since we know all sides of this square are the same, that means imaginary segment AD would also be 12. And in an equilateral triangle, all sides are the same. So we know this five-sided figure has a perimeter of 12 + 12 + 12 + 12 + 12 = 60.
Top
Master | Next Rank: 500 Posts
Posts: 139
Joined: Fri Nov 26, 2010 4:45 pm
Location: Boston
Thanked: 20 times
Followed by:1 members
GMAT Score:720

by stormier » Tue Jan 11, 2011 12:02 pm
steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

Image

Draw an Imaginary line to join the points A and D. Now AD must be parallel to BC (since angles ABC and DCB are both 90 deg and both BA and CD measure 12).

Also, angle BAD = angle CDA = 90 degrees.

Angle EAD = 90-30 = 60
Angle ADE = 90-30 = 60

Triangle ADE is an equilateral triangle. Thus AE = ED = AD = 12
Perimeter = 12*5 = 60
Top
Master | Next Rank: 500 Posts
Posts: 181
Joined: Sat Oct 16, 2010 1:57 pm
Thanked: 4 times

by N:Dure » Tue Jan 11, 2011 2:51 pm
The apparent is the 12+12+12 sides

Now since AED is equilateral, then AE=ED= 12

Perimeter = 12 * 5 = 60
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Tue Jan 11, 2011 11:14 pm
aleph777 wrote:Hi Steven,

We're given three segments already, so we just need to solve for segments AE and ED.

The clue here is in the 30-degree angles we're given. Imagine that AED were a triangle, and then locate the angle of DAE based on the fact that DAB is 90 degrees and BAE is 30. 90 - 30 = 60. And the same goes for angle ADE. Which makes this an equilateral triangle.

Since we know all sides of this square are the same, that means imaginary segment AD would also be 12. And in an equilateral triangle, all sides are the same. So we know this five-sided figure has a perimeter of 12 + 12 + 12 + 12 + 12 = 60.
Hey Aleph. Some Doubts:

Angle DAB =90 . How?

Why would AD be 12. CAn we imagine this figure to be a square?

Thanx.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Tue Jan 11, 2011 11:17 pm
stormier wrote:
steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

Image

Draw an Imaginary line to join the points A and D. Now AD must be parallel to BC (since angles ABC and DCB are both 90 deg and both BA and CD measure 12).

Also, angle BAD = angle CDA = 90 degrees.

Angle EAD = 90-30 = 60
Angle ADE = 90-30 = 60

Triangle ADE is an equilateral triangle. Thus AE = ED = AD = 12
Perimeter = 12*5 = 60
How can we say that AD is parallel to BC. Ur reasoning: (since angles ABC and DCB are both 90 deg and both BA and CD measure 12). Is this sum kind of theorem. Kindly explain.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Jan 12, 2011 3:57 am
ankur.agrawal wrote:
stormier wrote:
steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

Image

Draw an Imaginary line to join the points A and D. Now AD must be parallel to BC (since angles ABC and DCB are both 90 deg and both BA and CD measure 12).

Also, angle BAD = angle CDA = 90 degrees.

Angle EAD = 90-30 = 60
Angle ADE = 90-30 = 60

Triangle ADE is an equilateral triangle. Thus AE = ED = AD = 12
Perimeter = 12*5 = 60
How can we say that AD is parallel to BC. Ur reasoning: (since angles ABC and DCB are both 90 deg and both BA and CD measure 12). Is this sum kind of theorem. Kindly explain.
Here is one way to prove that ABCD is square:
Draw diagonals AC and BD.
Since AB = BC = 12 and angle ABC is a right angle, diagonal AC = 12√2, forming a 45:45:90 triangle.
Since BC = CD = 12 and angle BCD is a right angle, diagonal BD = 12√2, forming another 45:45:90 triangle.
The result is that diagonals AC and BD are both equal and perpendicular, proving that ABCD is a square. A square is the only quadrilateral in which the diagonals are equal and perpendicular.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Wed Jan 12, 2011 11:19 pm
GMATGuruNY wrote:
ankur.agrawal wrote:
stormier wrote:
steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

Image

Draw an Imaginary line to join the points A and D. Now AD must be parallel to BC (since angles ABC and DCB are both 90 deg and both BA and CD measure 12).

Also, angle BAD = angle CDA = 90 degrees.

Angle EAD = 90-30 = 60
Angle ADE = 90-30 = 60

Triangle ADE is an equilateral triangle. Thus AE = ED = AD = 12
Perimeter = 12*5 = 60
How can we say that AD is parallel to BC. Ur reasoning: (since angles ABC and DCB are both 90 deg and both BA and CD measure 12). Is this sum kind of theorem. Kindly explain.
Here is one way to prove that ABCD is square:
Draw diagonals AC and BD.
Since AB = BC = 12 and angle ABC is a right angle, diagonal AC = 12√2, forming a 45:45:90 triangle.
Since BC = CD = 12 and angle BCD is a right angle, diagonal BD = 12√2, forming another 45:45:90 triangle.
The result is that diagonals AC and BD are both equal and perpendicular, proving that ABCD is a square. A square is the only quadrilateral in which the diagonals are equal and perpendicular.
Why will they be perpendicular? Plz clear my doubt
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Jan 13, 2011 12:36 am
ankur.agrawal wrote:
GMATGuruNY wrote:
ankur.agrawal wrote:
stormier wrote:
steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

Image

Draw an Imaginary line to join the points A and D. Now AD must be parallel to BC (since angles ABC and DCB are both 90 deg and both BA and CD measure 12).

Also, angle BAD = angle CDA = 90 degrees.

Angle EAD = 90-30 = 60
Angle ADE = 90-30 = 60

Triangle ADE is an equilateral triangle. Thus AE = ED = AD = 12
Perimeter = 12*5 = 60
How can we say that AD is parallel to BC. Ur reasoning: (since angles ABC and DCB are both 90 deg and both BA and CD measure 12). Is this sum kind of theorem. Kindly explain.
Here is one way to prove that ABCD is square:
Draw diagonals AC and BD.
Since AB = BC = 12 and angle ABC is a right angle, diagonal AC = 12√2, forming a 45:45:90 triangle.
Since BC = CD = 12 and angle BCD is a right angle, diagonal BD = 12√2, forming another 45:45:90 triangle.
The result is that diagonals AC and BD are both equal and perpendicular, proving that ABCD is a square. A square is the only quadrilateral in which the diagonals are equal and perpendicular.
Why will they be perpendicular? Plz clear my doubt
Image

The drawing above shows the 45:45:90 triangles that are formed when the diagonals AC and BD are drawn. It illustrates why the diagonals both equal and perpendicular, proving that ABCD is a square. Please refer to the explanation in my earlier post.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Thu Jan 13, 2011 12:41 am
GMATGuruNY wrote:
ankur.agrawal wrote:
GMATGuruNY wrote:
ankur.agrawal wrote:
stormier wrote:
steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

Image

Draw an Imaginary line to join the points A and D. Now AD must be parallel to BC (since angles ABC and DCB are both 90 deg and both BA and CD measure 12).

Also, angle BAD = angle CDA = 90 degrees.

Angle EAD = 90-30 = 60
Angle ADE = 90-30 = 60

Triangle ADE is an equilateral triangle. Thus AE = ED = AD = 12
Perimeter = 12*5 = 60
How can we say that AD is parallel to BC. Ur reasoning: (since angles ABC and DCB are both 90 deg and both BA and CD measure 12). Is this sum kind of theorem. Kindly explain.
Here is one way to prove that ABCD is square:
Draw diagonals AC and BD.
Since AB = BC = 12 and angle ABC is a right angle, diagonal AC = 12√2, forming a 45:45:90 triangle.
Since BC = CD = 12 and angle BCD is a right angle, diagonal BD = 12√2, forming another 45:45:90 triangle.
The result is that diagonals AC and BD are both equal and perpendicular, proving that ABCD is a square. A square is the only quadrilateral in which the diagonals are equal and perpendicular.
Why will they be perpendicular? Plz clear my doubt
Image

The drawing above shows the 45:45:90 triangles that are formed when the diagonals AC and BD are drawn. It illustrates why the diagonals both equal and perpendicular, proving that ABCD is a square. Please refer to the explanation in my earlier post.
Thanks for the explaination. Apology for asking small doubts.
Top
Post new topic Post Reply
• Page 1 of 1