Question

The length of one of the legs of a right triangle is 9. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the the larger of the two missing sides (the hypotenuse).

Answer 1

The length of the hypotenuse is 41.

Explanation:

Let x be the length of the other leg

x + 1 be the length of the hypotenuse

Using pythagorean theorem you'll have the equation,

`c^2 = a^2 + b^2\\(x+1)^2 = 9^2 + x^2\\x^2 + 2x + 1 = 81 + x^2\\x^2 - x^2 + 2x = 81 - 1\\2x = 80\\x = (80)/(2) \\x = 40`

Hypotenuse is x + 1

hypotenuse = 40 + 1

= 41