Find the length of the hypotenuse

The length of one leg of a right triangle is 5cm. The hypotenuse is 1cm more than the other leg. Find the length of the hypotenuse.

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Use the Pythagorean Theorem
a² + b² = c² {the sum of the squares of the legs is equal to the square of the hypotenuse}
a and b are the legs, and c is the hypotenuse

x = other leg
x + 1 = hypotenuse {the hypotenuse is 1 longer than the other leg}

the legs are x and 5, and the hypotenuse is x + 1

x² + 5² = (x + 1)² {substituted x and 5 in for a and b, and x + 1 in for c}
x² + 25 = (x + 1)(x + 1) {squared the x and the 5, and squared the binomial by multiplying by itself}
x² + 25 = x² + 2x + 1 {multiplied (x + 1) by (x + 1)}
25 = 2x + 1 {subtracted x² from each side}
24 = 2x {subtracted 1 from each side}
x = 12 {divided each side by 2}
x + 1 = 13 {substituted 12, in for x, into x + 1}

the hypotenuse, (x+ 1), is 13

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