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# If the hypotenuse of an isosceles right triangle is

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Senior RC Moderator
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
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Location: India
WE: General Management (Aerospace and Defense)
If the hypotenuse of an isosceles right triangle is [#permalink]

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22 Sep 2017, 15:13
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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
[Reveal] Spoiler: OA

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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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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 sides in ratio $$x: x: x\sqrt{2}$$

The hypotenuse = $$8\sqrt{2}$$
The legs' length is $$8$$.*

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.

$$x^2 + x^2 = (8\sqrt{2})^{2}$$
$$2x^2 = (64)(2)$$
$$x^2 = 64$$
$$x = 8$$
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If the hypotenuse of an isosceles right triangle is   [#permalink] 22 Sep 2017, 16:13
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