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# If the area of the shaded region of the square above is 20, what is th

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Math Expert
Joined: 02 Sep 2009
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If the area of the shaded region of the square above is 20, what is th  [#permalink]

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05 Jul 2018, 21:41
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77% (01:30) correct 23% (00:46) wrong based on 35 sessions

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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

Attachment:

2018-07-06_0839.png [ 6.51 KiB | Viewed 390 times ]

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Re: If the area of the shaded region of the square above is 20, what is th  [#permalink]

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05 Jul 2018, 22:03
Bunuel 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

Attachment:
2018-07-06_0839.png

Area of square=4* area of shaded region=4*20=80
The length of the sides of the square=$$\sqrt{80}$$=$$4\sqrt{5}$$
So, perimeter of the square=4*length of the sides of the square=4*$$4\sqrt{5}$$=$$16\sqrt{5}$$

Ans.(C)
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If the area of the shaded region of the square above is 20, what is th  [#permalink]

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06 Jul 2018, 09:24
Bunuel 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

Attachment:
2018-07-06_0839.png

The diagonals of a square divide it into 4 triangles of equal area.

Area of the square = $$s^2$$
$$\frac{1}{4}s^2=20$$
$$s^2=80$$
$$\sqrt{s^2}=\sqrt{16*5}$$
$$s=4\sqrt{5}$$

Perimeter = $$4s=(4*4\sqrt{5})=16\sqrt{5}$$

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Re: If the area of the shaded region of the square above is 20, what is th  [#permalink]

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06 Jul 2018, 11:25
Bunuel 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

Attachment:
2018-07-06_0839.png

$$\frac{1}{4}^{th}$$ of the square is $$20$$, so the area of the square is $$80$$, Thus each side must be $$\sqrt{80}$$

$$80 = 2^4*5$$

Since, $$a = \sqrt{80}$$

Or, $$a = 4\sqrt{5}$$

Thus, the perimeter of the square must be $$16\sqrt{5}$$, Answer must be (C)
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Abhishek....

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Re: If the area of the shaded region of the square above is 20, what is th &nbs [#permalink] 06 Jul 2018, 11:25
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