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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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New post 22 Sep 2017, 16:13
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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

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

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New post 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 \(\frac{8*8}{2} = 32\)

ANSWER C


*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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New post 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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