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Isosceles right triangle ABC and Square EFGH have the same a

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Isosceles right triangle ABC and Square EFGH have the same a [#permalink] New post 29 Oct 2017, 02:01
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83% (01:59) correct 16% (01:53) wrong based on 6 sessions
Isosceles right triangle ABC and Square EFGH have the same area.

Quantity A
Quantity B
Perimeter of ABC
Perimeter of EFGH



A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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[Reveal] Spoiler: OA
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Re: Isosceles right triangle ABC and Square EFGH have the same a [#permalink] New post 25 Nov 2017, 17:01
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Here we can set up the following equation with both Areas:

1) Triangle: (a^2)/2 = A
2) Sqaure: b^2 = A

A stands for Area, a for side of triangle and b for side of square.

If we solve these equations for the sides a and b respectively, we obtain the following

1) a^2 = 2A => a = sqRoot(2A)

2) b^2 = A => b =sqRoot (A)

Now we can set up perimeter equations with the comparable variable A

1) SqRoot2A * 3 => 3*SqRoot2A
2) SqRootA * 4 => 4*SQRootA

Hence the perimeter of the triangle is bigger than that of the square Therefore A>B

Last edited by simon1994 on 08 Dec 2017, 02:41, edited 2 times in total.
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Re: Isosceles right triangle ABC and Square EFGH have the same a [#permalink] New post 07 Dec 2017, 19:38
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simon1994 wrote:
Here we can set up the following equation with both Areas:

1) Triangle: (a^2)/2 = A
2) Sqaure: b^2 = A

A stands for Area, a for side of triangle and b for side of square.

If we solve these equations for the sides a and b respectively, we obtain the following

1) a^2 = 2A
2) b^2 = A

Now we can set up perimeter equations with the comparable variable A

1) 2A * 3 => 6A
2) A*4 => 4A

Hence the perimeter of the triangle(6A) is bigger than that of the square(4A) Therefore A>B


Would you explain why you put "2A * 3" and "A*4"
you times their area, this is also okay to compare their sides?

thank you !
2 KUDOS received
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Re: Isosceles right triangle ABC and Square EFGH have the same a [#permalink] New post 08 Dec 2017, 02:43
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wongpcla wrote:
simon1994 wrote:
Here we can set up the following equation with both Areas:

1) Triangle: (a^2)/2 = A
2) Sqaure: b^2 = A

A stands for Area, a for side of triangle and b for side of square.

If we solve these equations for the sides a and b respectively, we obtain the following

1) a^2 = 2A
2) b^2 = A

Now we can set up perimeter equations with the comparable variable A

1) 2A * 3 => 6A
2) A*4 => 4A

Hence the perimeter of the triangle(6A) is bigger than that of the square(4A) Therefore A>B


Would you explain why you put "2A * 3" and "A*4"
you times their area, this is also okay to compare their sides?

thank you !


Hi,

I changed by previous answer their was a slight mistake. However the reasoning remains the same.

Regarding your question: We need to obtain compare the Perimeter of a triangle with the perimeter of a square.

So we we have to multiply by 3 to obtain the perimeter of a triangle and by 4 to obtain the perimeter of a square.

Hope that helped!
Re: Isosceles right triangle ABC and Square EFGH have the same a   [#permalink] 08 Dec 2017, 02:43
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Isosceles right triangle ABC and Square EFGH have the same a

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