It's a quadratic word problem!

Question

Here is the problem: The height of a triangle measures one foot more than twice its base. The area of the triangle is 18 sq ft. Find the measures of the base and height of the triangle. Use the equation 18=b^2+0.5b to find the base, b, and height, h. 

 

A thorough explanation would be hightly advised. Thank you to anyone who can help me. :)

Answer 1

A=(1/2)(b)(h)

b=base

h=height

h=2b+1

A=(1/2)(b)(h)

18=(1/2)(b)(2b+1)

multiply both sides by 2

36=(b)(2b+1)

36=2b^2+b

2b^2+b-36=0

factor

(2b+9)(b-4)=0

b-4=0

b=4 feet

h=(2*4+1)=9 feet

check...

A=(1/2)(4)(9)

A=2*9

A=18 sq ft