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An isosceles right triangle has an area of 50. What is the length of

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Joined: 02 Sep 2009
Posts: 50004
An isosceles right triangle has an area of 50. What is the length of  [#permalink]

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21 Sep 2018, 01:19
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Difficulty:

15% (low)

Question Stats:

93% (00:59) correct 7% (00:43) wrong based on 27 sessions

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An isosceles right triangle has an area of 50. What is the length of the hypotenuse?

(A) $$5$$

(B) $$5\sqrt{2}$$

(C) $$5\sqrt{3}$$

(D) $$10$$

(E) $$10\sqrt{2}$$

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Re: An isosceles right triangle has an area of 50. What is the length of  [#permalink]

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21 Sep 2018, 01:28
Bunuel wrote:
An isosceles right triangle has an area of 50. What is the length of the hypotenuse?

(A) $$5$$

(B) $$5\sqrt{2}$$

(C) $$5\sqrt{3}$$

(D) $$10$$

(E) $$10\sqrt{2}$$

Let, Side of isosceles triangle be x

Area $$= (1/2)*x*x = 50$$
i.e. $$x^2 = 100$$

i.e. $$x = 10$$

Hypotenuse = $$x√2 = 10√2$$

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Re: An isosceles right triangle has an area of 50. What is the length of  [#permalink]

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22 Sep 2018, 04:04

Solution

Given:
• An isosceles right triangle has an area of 50

To find:
• The length of the hypotenuse of the triangle

Approach and Working:
In an isosceles right-angle triangle, the angles are in the ratio 45 – 45 – 90.
Hence, the side ratio is 1: 1: √2
• So, we can assume the sides as a, a, and a√2

Now, we can write ½ x a x a = 50
• Or, a2 = 100, implies a = 10
• Therefore, hypotenuse = a√2 = 10√2

Hence, the correct answer is option E.

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Re: An isosceles right triangle has an area of 50. What is the length of &nbs [#permalink] 22 Sep 2018, 04:04
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