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# If the hypotenuse of an isosceles right triangle is

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

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22 Sep 2017, 16:13
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88% (01:04) correct 12% (01:06) wrong based on 42 sessions

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If the hypotenuse of an isosceles right triangle is $$8\sqrt{2}$$ , what is the area of the triangle?

(A) 18
(B) 24
(C) 32
(D) 48
(E) 64

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

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22 Sep 2017, 17:13
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Gnpth wrote:
If the hypotenuse of an isosceles right triangle is $$8\sqrt{2}$$ , what is the area of the triangle?

(A) 18
(B) 24
(C) 32
(D) 48
(E) 64

An isosceles right triangle has angle measures of 45-45-90,
and corresponding sides opposite those angles in ratio $$x: x: x\sqrt{2}$$

The hypotenuse = $$8\sqrt{2}$$ and corresponds with $$x\sqrt{2}$$
Simply divide by $$\sqrt{2}$$ to get $$x$$, which equals the legs' length

The legs' length, $$x = 8$$.*

And area is $$\frac{8*8}{2} = 32$$

*If it isn't clear, from the ratio of sides, that side length = x = 8, or if you don't recognize that triangle, you can use the Pythagorean theorem to find side length (then area). It is a right triangle, and its sides are equal. Side, $$s = x$$ (easier to see the ratio derivation)

$$x^2 + x^2 = (8\sqrt{2})^{2}$$
$$2x^2 = (64)(2)$$
$$x^2 = 64$$
$$x = 8$$
Area: $$\frac{b*h}{2}=\frac{8*8}{2}=32$$
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Re: If the hypotenuse of an isosceles right triangle is  [#permalink]

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02 Aug 2019, 16:46
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Re: If the hypotenuse of an isosceles right triangle is   [#permalink] 02 Aug 2019, 16:46
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