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# If the hypotenuse of an isosceles right triangle has length of 8, then

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If the hypotenuse of an isosceles right triangle has length of 8, then  [#permalink]

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18 Oct 2018, 00:53
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Difficulty:

25% (medium)

Question Stats:

71% (01:00) correct 29% (00:30) wrong based on 42 sessions

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If the hypotenuse of an isosceles right triangle has length of 8, then the area of the triangle is

A. 4
B. 4√2
C. 8
D. 8√2
E. 16

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If the hypotenuse of an isosceles right triangle has length of 8, then  [#permalink]

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18 Oct 2018, 01:01
Bunuel wrote:
If the hypotenuse of an isosceles right triangle has length of 8, then the area of the triangle is

A. 4
B. 4√2
C. 8
D. 8√2
E. 16

An isosceles right triangle has angle 45-45-90, whose sides are in the ratio $$1:1:\sqrt{2}$$

As the hypotenuse of the isosceles triangle is 8, the other sides measure $$\frac{8}{\sqrt{2}}$$ = base = height

Therefore, the area for this triangle is $$\frac{1}{2}*\frac{8}{\sqrt{2}}*\frac{8}{\sqrt{2}} = \frac{64}{4} = 16$$(Option E)
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If the hypotenuse of an isosceles right triangle has length of 8, then &nbs [#permalink] 18 Oct 2018, 01:01
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