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.

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.

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step-by-step explanation:

yes i have heard the tea

i believe both

no, tati didnt over exaggerate

james might might idk and tbh dont rly care