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

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Math Expert
Joined: 02 Sep 2009
Posts: 55803
What is the length of the hypotenuse of an isosceles right triangle of  [#permalink]

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25 Dec 2018, 08:45
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Difficulty:

15% (low)

Question Stats:

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

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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. $$8\sqrt{3}$$

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

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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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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.

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

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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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