Question

A triangle has an area of 64 square feet. If the height of the triangle is 8 feet more than its base, x, what are its height and base?

Answer 1

Answer:

8 feet

Step-by-step explanation:

Given data

Area= 64 square feet

Base= x feet

Height= x+8 feet

The expression for the area

A= 1/2b*h

substitute

64= 1/2*x*(x+8)

64= 1/2*x^2+8x

64= (x^2+8x)/2

cross multiply

64*2= x^2+8x

128= x^2+8x

rearrange

x^2+8x-128= 0

using the quadratic formula

a=1

b=8

c=-128

x= -b±√b^2-4ac/2a

x= -1±√8^2-4*1*-128/2*1

simplifying

x= 8

x=-16

Hence the height of the base is

h= 8 feet