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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE Math Challenge #108-If the area of the shaded region [#permalink]
Expert's post 00:00

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions 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]
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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Manager Joined: 27 Sep 2017
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Re: GRE Math Challenge #108-If the area of the shaded region [#permalink]
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?
Director  Joined: 07 Jan 2018
Posts: 598
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Kudos [?]: 538 , given: 88

Re: GRE Math Challenge #108-If the area of the shaded region [#permalink]
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

No image only icon
Intern Joined: 08 Apr 2018
Posts: 44
Followers: 0

Kudos [?]: 15 , given: 16

Re: GRE Math Challenge #108-If the area of the shaded region [#permalink]
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

the image no longer exists so I cant view it.
Director Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 21 , given: 1

Re: GRE Math Challenge #108-If the area of the shaded region [#permalink]
No image. Re: GRE Math Challenge #108-If the area of the shaded region   [#permalink] 16 Jan 2019, 22:40
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