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# In a certain isosceles right triangle, the altitude to the hypotenuse has length . What is the area of the triangle?

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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

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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