The hypotenuse of a right triangle is 13ft long. The longer leg is 7ft longer than the shorter leg. Find the side lengths of the triangle.

The side lengths are 5, 12, 13

Step-by-step explanation:

These are the side lengths we know before we have solved the problem.

a= x   b= x+7   c= 13

If we put this into the Pythagorean theorem, we get

Expand

Subtract 169 from both sides

Solve using the quadratic formula

a= 2   b= 14   c= -120

If we separate the solutions we get

and

Since this is a question about length, we can ignore the negative.

So the longer leg is 12ft and the shorter leg is 5ft

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step-by-step explanation: