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The area of square ABDE in the figure above is 100. If BC = CD, what

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The area of square ABDE in the figure above is 100. If BC = CD, what  [#permalink]

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New post 11 Nov 2017, 05:41
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The area of square ABDE in the figure above is 100. If BC = CD, what is the perimeter of ∆ BCD?

(A) 5√2 + 10
(B) 20
(C) 10√2 + 10
(D) 30
(E) 20√2 + 10


Attachment:
2017-11-10_1035_001.png
2017-11-10_1035_001.png [ 4.73 KiB | Viewed 647 times ]

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The area of square ABDE in the figure above is 100. If BC = CD, what  [#permalink]

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New post 11 Nov 2017, 07:44
Bunuel wrote:
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The area of square ABDE in the figure above is 100. If BC = CD, what is the perimeter of ∆ BCD?

(A) 5√2 + 10
(B) 20
(C) 10√2 + 10
(D) 30
(E) 20√2 + 10


Attachment:
2017-11-10_1035_001.png

Area of square = s\(^2\) = 100
s = 10
BD = 10

∆ BCD has a right angle and two equals sides (BC = CD).
∆ BCD is a right isosceles triangle with side lengths in ratio \(x: x: x\sqrt{2}\)

Sides BC and CD correspond with \(x\)
Side BD corresponds with \(x\sqrt{2}\)

\(x\sqrt{2} = 10\)

\(x =\frac{10}{\sqrt{2}}\)

\(x=\frac{10}{\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}=\frac{10\sqrt{2}}{2}=5\sqrt{2}\)

\(x=5\sqrt{2}\) = BC = CD

Perimeter P of ∆ BCD = BC + CD + BD

P = \(5\sqrt{2} + 5\sqrt{2} + 10 =\)
P = \(10\sqrt{2} + 10\)

Answer C
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The area of square ABDE in the figure above is 100. If BC = CD, what &nbs [#permalink] 11 Nov 2017, 07:44
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The area of square ABDE in the figure above is 100. If BC = CD, what

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