Question

The hypotenuse of a right triangle is 95 inches long. One leg is 4 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest tenth of an inch.

Answer 1

65.1 and 69.1

Explanation:

c² = a² + b²

c= 95

a - one leg

b= (a + 4) - second leg

95² = a² + (a + 4)²

9025 = a² + a² + 2*4a + 16

2a² + 8a - 9009 = 0

`a= (-b +/-√(b^2 - 4ac) )/(2a) \\\\a = (-8 +/-√(8^2 - 4*2*9009) )/(2*2) \\\\a=65.1 \ and \ a=- 69.1`

A leg length can be only positive. a = 65.1

b = 65.1 + 4 = 69.1

Answer 2

65.1 and 69.1

Explanation:

a^2+b^2=c^2

c=95

b=a+4

Solve for a^2+(a+4)^2=95^2

a=65.1

b=a+4=69.1