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GRE Math Challenge #108-If the area of the shaded region

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GMAT Club Legend
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GRE Math Challenge #108-If the area of the shaded region [#permalink] New post 15 May 2015, 11:53
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Image

If the area of the shaded region of the square above is 20, what is the perimeter of the square?

(A) 4 \(\sqrt{5}\)
(B) 8 \(\sqrt{5}\)
(C) 16 \(\sqrt{5}\)
(D) 80
(E) 400
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #108-If the area of the shaded region [#permalink] New post 19 Dec 2017, 07:14
sandy wrote:

If the area of the shaded region of the square above is 20, what is the perimeter of the square?

(A) 4 \(\sqrt{5}\)
(B) 8 \(\sqrt{5}\)
(C) 16 \(\sqrt{5}\)
(D) 80
(E) 400



Here,

The figure is a square and the two diagonals divide the square into 4 equal triangle.

Let the length of the square = x

Area of the shaded triangles = 1/2 * Length * Altitude

= \(\frac{1}{2} * x * \frac{x}{2}\) ( height of the triangle is half of length x, since the diagonal of a square cuts each other at equal distance )
= \(\frac{(x^2)}{4}\)

But the area of the shaded triangle = 20

therefore \(\frac{(x^2)}{4}\) = 20

or x = \(4\sqrt{5}\)

Perimeter of Square = 4 * x

= 4 * \(4\sqrt{5}\)
= 16 \(\sqrt{5}\)
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Re: GRE Math Challenge #108-If the area of the shaded region [#permalink] New post 19 Dec 2017, 17:31
pranab01 wrote:
sandy wrote:

If the area of the shaded region of the square above is 20, what is the perimeter of the square?

(A) 4 \(\sqrt{5}\)
(B) 8 \(\sqrt{5}\)
(C) 16 \(\sqrt{5}\)
(D) 80
(E) 400



Here,

The figure is a square and the two diagonals divide the square into 4 equal triangle.

Let the length of the square = x

Area of the shaded triangles = 1/2 * Length * Altitude

= \(\frac{1}{2} * x * \frac{x}{2}\) ( height of the triangle is half of length x, since the diagonal of a square cuts each other at equal distance )
= \(\frac{(x^2)}{4}\)

But the area of the shaded triangle = 20

therefore \(\frac{(x^2)}{4}\) = 20

or x = \(4\sqrt{5}\)

Perimeter of Square = 4 * x

= 4 * \(4\sqrt{5}\)
= 16 \(\sqrt{5}\)


Hi, sorry to bother, I can not see the pic, would you show me that?
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Re: GRE Math Challenge #108-If the area of the shaded region [#permalink] New post 08 Mar 2018, 00:59
sandy wrote:
Image

If the area of the shaded region of the square above is 20, what is the perimeter of the square?

(A) 4 \(\sqrt{5}\)
(B) 8 \(\sqrt{5}\)
(C) 16 \(\sqrt{5}\)
(D) 80
(E) 400


No image only icon
Intern
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Re: GRE Math Challenge #108-If the area of the shaded region [#permalink] New post 08 Jul 2018, 19:47
sandy wrote:
Image

If the area of the shaded region of the square above is 20, what is the perimeter of the square?

(A) 4 \(\sqrt{5}\)
(B) 8 \(\sqrt{5}\)
(C) 16 \(\sqrt{5}\)
(D) 80
(E) 400

the image no longer exists so I cant view it.
Re: GRE Math Challenge #108-If the area of the shaded region   [#permalink] 08 Jul 2018, 19:47
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GRE Math Challenge #108-If the area of the shaded region

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