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Area when sides are 12 and 8

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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
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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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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:

Image

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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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:

Image

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?
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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.
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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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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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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:

Image

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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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:

Image

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 = (s²/4)√3.
The area of an equilateral triangle with a perimeter of 12 = (4²/4)√3 ≈ 6.8, which is greater than 6.
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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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