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## 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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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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Mathematics
2 weeks
2021-09-05T13:24:29+00:00
2021-09-05T13:24:29+00:00 2 Answers
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## Answers ( )

Answer: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 !

Answer: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

aandbare the side lengths andcis the hypotenuse.The hypotenuse is 13 and the legs are

xand (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.