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What is the length of the hypotenuse of an isosceles right triangle of

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What is the length of the hypotenuse of an isosceles right triangle of  [#permalink]

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New post 25 Dec 2018, 08:45
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (01:11) correct 23% (01:06) wrong based on 59 sessions

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Re: What is the length of the hypotenuse of an isosceles right triangle of  [#permalink]

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New post 25 Dec 2018, 09:21
Bunuel wrote:
What is the length of the hypotenuse of an isosceles right triangle of area 32?


A. 4

B. \(4\sqrt{2}\)

C. 8

D. \(8\sqrt{2}\)

E. \(8\sqrt{3}\)



x^2=32*2
x=8

64+64 = 128 = sqrt 128 = hypotenuse

or say 8 sqrt 2
IMO D
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Re: What is the length of the hypotenuse of an isosceles right triangle of  [#permalink]

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New post 26 Dec 2018, 11:01

Solution



Given:
    • The area of an isosceles right-angle triangle is 32

To find:
    • The length of the hypotenuse

Approach and Working:
Let us assume the length of each of the equal sides of the triangle is n.
Hence, the area = \(\frac{1}{2}\) x n x n = 32
    Or, \(n^2\) = 64
    Or, n = 8

Therefore, the length of the hypotenuse = \(\sqrt{8^2 + 8^2} = 8\sqrt{2}\)

Hence, the correct answer is option D.

Answer: D

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Re: What is the length of the hypotenuse of an isosceles right triangle of  [#permalink]

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New post 26 Dec 2018, 18:44
Bunuel wrote:
What is the length of the hypotenuse of an isosceles right triangle of area 32?


A. 4

B. \(4\sqrt{2}\)

C. 8

D. \(8\sqrt{2}\)

E. \(8\sqrt{3}\)



Isosceles right angled triangle will have two sides equal, say, x.

\(Area =(\frac{1}{2})*x*x=32, x^2=64, x=8.\)

Let hypotenuse be y.
Using Pythagoras theorem,
\(x^2+x^2=y^2\)
or \(y=\sqrt{2}*x=8\sqrt{2}\)
IMO, Option D.
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Re: What is the length of the hypotenuse of an isosceles right triangle of   [#permalink] 26 Dec 2018, 18:44
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