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16 November, 02:06

The area of a right triangle is 270 square meters. The height of the right triangle is 15 meters.

What is the length of the hypotenuse of the right triangle?

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  1. 16 November, 02:52
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    To solve this, we find the measure of the base using the the formula for the area of a triangle. Then plug both of these into the Pythagorean theorem to solve for the hypotenuse.

    Area of a triangle = 1/2 * base * height

    270 = 1/2 * 15 * base

    270 = (15 / 2) (base)

    270 (2 / 15) = base

    540 / 15 = base

    36 = base

    Now, we plug into the Pythagorean Theorem of a² + b² = c² where a and b are the legs of the triangle (AKA the base and height) and c is the hypotenuse.

    15² + 36² = c²

    225 + 1296 = c²

    1521 = c²

    √c² = √1521

    c = √1521

    c = 39

    The length of your hypotenuse is 39 meters.
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