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

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Math Expert
Joined: 02 Sep 2009
Posts: 53721
If the hypotenuse of an isosceles right triangle has length of 8, then  [#permalink]

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18 Oct 2018, 01:53
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Difficulty:

15% (low)

Question Stats:

81% (01:16) correct 19% (00:56) wrong based on 50 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, 02:01
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   [#permalink] 18 Oct 2018, 02:01
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