Area when sides are 12 and 8

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saxenashobhit: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Aug 07, 2010 8:53 pmFollowed by: 1 member; Thanked: 1 times

by saxenashobhit » Thu Jul 07, 2011 5:15 am

If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?

I 35
II 48
III 56

I only

I and II only

I and III only

II and III only

I, II, and III

Kaplan quiz 6 question 4 - https://www.scribd.com/doc/58999877/GMAT ... et-6-Quant

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jul 07, 2011 6:28 am

Hi,
If a,b,c are the sides of triangle ABC, then area of triangle is given by (1/2)b*c*sine A
So, area is (1/2)*8*12*sine A = 48 sine A
As 0 < sine A <= 1
area is less than or equal to 48

Hence, B

Cheers!

Things are not what they appear to be... nor are they otherwise

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goalevan: Master | Next Rank: 500 Posts; Posts: 111; Joined: Tue Dec 30, 2008 1:25 pm; Location: USA; Thanked: 28 times; GMAT Score:770

by goalevan » Sat Jul 09, 2011 3:34 pm

1/2 * base * height = area

The triangle with maximum area having sides of 12 and 8 will be a right triangle with these lengths as the legs.

Area <= 1/2 * 12 * 8 = 48

I and II satisfy.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 10, 2011 3:57 am

saxenashobhit wrote:If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?

I 35
II 48
III 56

I only

I and II only

I and III only

II and III only

I, II, and III

Kaplan quiz 6 question 4 - https://www.scribd.com/doc/58999877/GMAT ... et-6-Quant

Given 2 sides of a triangle, the maximum possible area will be achieved when a right angle is placed between them so that one side becomes the base, while the other side becomes the corresponding height.

This will hold true for any triangle for which we've been given 2 sides.

Given a side of 12 and a side of 8, the drawings below illustrate why the maximum possible area is 48:

The correct answer is B.

Last edited by GMATGuruNY on Sat Jul 16, 2011 2:35 am, edited 1 time in total.

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krishnasty: Master | Next Rank: 500 Posts; Posts: 142; Joined: Mon Jan 10, 2011 8:03 am; Thanked: 19 times

by krishnasty » Sun Jul 10, 2011 4:43 am

GMATGuruNY wrote:
saxenashobhit wrote:If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?

I 35
II 48
III 56

I only

I and II only

I and III only

II and III only

I, II, and III

Kaplan quiz 6 question 4 - https://www.scribd.com/doc/58999877/GMAT ... et-6-Quant
Given 2 sides of a triangle, the maximum possible area will be achieved when a right angle is placed between them so that one side becomes the base, while the other side becomes the corresponding height.

Given a side of 12 and a side of 8, the drawings below illustrate why the maximum possible area is 48:

The correct answer is B.

Is this applicable to every triangle? does the area of a triangle is max when the triangle is a right angled triangle?

---------------------------------------
Appreciation in thanks please!!

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KapTeacherEli: GMAT Instructor; Posts: 578; Joined: Tue Aug 25, 2009 6:00 pmFollowed by: 62 members; Thanked: 136 times

by KapTeacherEli » Sun Jul 10, 2011 5:12 pm

krishnasty wrote: Is this applicable to every triangle? does the area of a triangle is max when the triangle is a right angled triangle?

Yup. Any time you have two sides, the greatest possible area of the triangle will be the one with 90 degress between them.

Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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ArpanaAmishi: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Sun Jun 06, 2010 10:52 pmFollowed by: 1 member; Thanked: 2 times

by ArpanaAmishi » Mon Jul 11, 2011 12:43 am

I am little confused..from where 'max area' comes in picture...question is not looking for max area...Please clarify.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 11, 2011 3:27 am

ArpanaAmishi wrote:I am little confused..from where 'max area' comes in picture...question is not looking for max area...Please clarify.

To determine whether I,II and III could be the area, we need to determine the maximum possible area.
Since the area can't be more than 48, we can eliminate any answer choice that includes III, which says that the area could be 56.
Eliminate C,D and E.
Since the area can be 48, the correct answer must include II.
Eliminate A.
The correct answer is B.

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patanjali.purpose: Legendary Member; Posts: 784; Joined: Sun Apr 03, 2011 3:51 amFollowed by: 12 members; Thanked: 114 times

by patanjali.purpose » Fri Sep 02, 2011 11:52 pm

krishnasty wrote:
GMATGuruNY wrote:
saxenashobhit wrote:If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?

I 35
II 48
III 56

I only

I and II only

I and III only

II and III only

I, II, and III

Kaplan quiz 6 question 4 - https://www.scribd.com/doc/58999877/GMAT ... et-6-Quant
Given 2 sides of a triangle, the maximum possible area will be achieved when a right angle is placed between them so that one side becomes the base, while the other side becomes the corresponding height.

Given a side of 12 and a side of 8, the drawings below illustrate why the maximum possible area is 48:

The correct answer is B.
Is this applicable to every triangle? does the area of a triangle is max when the triangle is a right angled triangle?

I think this is true only when 2 sides of a triangle is given. However, if we have been given perimeter of a triangle, for maximum possible area triangle need to be EQUILATERAL

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 03, 2011 2:38 am

patanjali.purpose wrote:
krishnasty wrote:
GMATGuruNY wrote:
saxenashobhit wrote:If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?

I 35
II 48
III 56

I only

I and II only

I and III only

II and III only

I, II, and III

Kaplan quiz 6 question 4 - https://www.scribd.com/doc/58999877/GMAT ... et-6-Quant
Given 2 sides of a triangle, the maximum possible area will be achieved when a right angle is placed between them so that one side becomes the base, while the other side becomes the corresponding height.

Given a side of 12 and a side of 8, the drawings below illustrate why the maximum possible area is 48:

The correct answer is B.
Is this applicable to every triangle? does the area of a triangle is max when the triangle is a right angled triangle?
I think this is true only when 2 sides of a triangle is given. However, if we have been given perimeter of a triangle, for maximum possible area triangle need to be EQUILATERAL

Correct!
Given TWO SIDES of a triangle, we will yield the maximum possible area by placing a RIGHT ANGLE between the two sides so that one of the two sides becomes the base, while the other becomes the height.
Given the PERIMETER of a triangle, we will yield the maximum possible area if the triangle is EQUILATERAL.

To illustrate:
Given sides of 3 and 4, the maximum possible area = (1/2)*3*4 = 6.
Perimeter = 3+4+5 = 12.
The area of an equilateral triangle = (sÂ²/4)âˆš3.
The area of an equilateral triangle with a perimeter of 12 = (4Â²/4)âˆš3 â‰ˆ 6.8, which is greater than 6.

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AbhiJ: Master | Next Rank: 500 Posts; Posts: 381; Joined: Wed May 19, 2010 10:15 pmFollowed by: 2 members; Thanked: 41 times

by AbhiJ » Mon Sep 05, 2011 2:29 am

Rather than remembering this as a rule better would be to visualise the solution. In right angled triangle the largest side would be the hypotaneous. Now try to increase, decrease size of hypotaneous by keeping 12, 8 fixed and rotating the included angle, thus as to increase,decrease the length of the hypotaneous. In either case, the effective height of the triangle decreases reducing the area.

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