hypotenuse

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lula lula
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hypotenuse

The hypotenuse of a right triangle is four times the length of one of the legs. The length of the other leg is √1215 feet. Find the lengths of the leg and hypotenuse.
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Re: hypotenuse

x = one of the legs
√1215 = other leg
4x = hypotenuse   {hypotenuse is four times the length of one of the legs}

a² + b² = c²   {Pythagorean Theorem}
a and b are the legs and c is the hypotenuse

x² + (√1215)² = (4x)²   {substituted into Pythagorean Theorem}
x² + 1215 = 16x²   {evaluated exponents}
1215 = 15x²   {subtracted x² from each side}
x² = 81   {divided each side by 15}
x = 9   {took square root of each side}
4x = 36   {substituted 9, in for x, into 4x}

one leg is 9
hypotenuse is 36


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