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GRE Math Challenge #108-If the area of the shaded region
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15 May 2015, 11:53
15 May 2015, 11:53
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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
Re: GRE Math Challenge #108-If the area of the shaded region
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19 Dec 2017, 07:14
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 \(\sqrt{5}\)
Re: GRE Math Challenge #108-If the area of the shaded region
[#permalink]
19 Dec 2017, 17:31
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?
