The hypotenuse of a right triangle is one inch longer than the longer leg. The shorter leg is seven inches shorter than the longer leg. Find the length of the hypotenuse.

Length of hypotenuse is 13 unit or 5 unit

Step-by-step explanation:

Find;

Length of hypotenuse

Computation;

Assume;

Length of hypotenuse = h

Length of longer leg = h - 1

Length of shorter leg = h - 1 - 7

Using Pythagorean theorem

hypotenuse² = longer leg² + shorter leg²  

h² = (h - 1)² + (h - 1 - 7)²  

h² = (h - 1)² + (h - 8)²  

h² = h² - 2h + 1 + h² - 16h + 64  

h² = 2h² - 18h + 65

h² - 18h + 65 = 0

h² - 13h - 5h + 65 = 0

h(h - 13) -5(h - 13)

(h - 13)(h - 5)

So,

Length of hypotenuse is 13 unit or 5 unit

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