The hypotenuse of a right triangle is 8 cm long. one leg is 2 cm longer than the other. find the length of the longer leg to the nearest tenth.

General formula to find the sides of right triangle is

a² + b² = c²

c stands for the hypotenuse

We can assume a stands for the shorter leg and b is the longer leg, the equation will be

b = a + 2

a = b - 2

Now input the number to the formula

a² + b² = c²

(b-2) ² + b² = 8²

b² - 4b + 4 + b² = 64

2b² - 4b + 4 - 64 = 0

2b² - 4b - 60 = 0

b² - 2b - 30 = 0

Work the equation by completing the square

b² - 2b - 30 = 0

b² - 2b = 30

b² - 2b + 1 = 30 + 1

(b + 1) ² = 31

b + 1 = √31

b = - 1 + √31

b = - 1 + 5.5678

b = 4.5678

b = 4.6

The longer leg is approximately 4.6