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In a certain isosceles right triangle, the altitude to the hypotenuse has length \(4\sqrt2\). What is the area of the triangle?

 Sep 1, 2018
 #1
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If the right triangle is isosceles, the two legs must be equal. By using Pythagorean Theorem, we can get \(2(a^2) = (4\sqrt{2})^2\) which equals \(2(a^2) = 32\). So \(a^2 = 16\). This gives us \(a = 4\). If the legs of the triangle are \(4\), we can get the area to be \(8\).

 

- Daisy

 Sep 1, 2018

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