Problem Solving

Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

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.

steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

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

The apparent is the 12+12+12 sides

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

Perimeter = 12 * 5 = 60

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.

stormier wrote:

steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

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.

ankur.agrawal wrote:

stormier wrote:

steven_ghoos wrote:Can someone explain me how to solve this one? Thanks

What is the perimeter of ABCDE?

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.

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?

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

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?

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

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.

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?

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

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.