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

Question

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

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4 months 2021-09-05T13:24:29+00:00 2 Answers 32 views 0

## Answers ( )

Step-by-step explanation:

Let x be the longer leg.

Then the shorter leg is (x-7) centimeters long.

According to the Pythagorean theorem,

x%5E2 + %28x-7%29%5E2 = 13%5E2,   or

x%5E2+%2B+x%5E2+-+14x+%2B+49 = 169

2x%5E2+-+14x+-+120 = 0

x%5E2+-+7x+%2B+60 = 0

Factor the quadratic polynomial

(x-12)*(x+5) = 0.

Its roots are x= 12 and  x= -5,  but only positive solution is meaningful.

ANSWER.  The longer leg is 12 cm;  the shorter leg is  12-7 = 5 cm.

CHECK.   12%5E2 + 5%5E2 = 144 + 25 = 169 = 13%5E2.    ! Correct !

The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.

Step-by-step explanation:

Let the shorter leg be x.

Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (x + 7).

Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by: Where a and b are the side lengths and c is the hypotenuse.

The hypotenuse is 13 and the legs are x and (x + 7). Substitute: Square: Simplify: We can divide both sides by two: Factor: Zero Product Property: Solve for each case: Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is: The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.