algebra word problem

Question

The length of a rectangle is 9 yd more than twicee the width x. The area is 980 yd2. part one write an equation in termsof x that represents the given relationship. part 2 solve the equation to find the dimensions of the given shape. part 3 the length is ___ yd?

Answer 1

width = x

length = 2x + 9

 

area = length x width

980 = (2x + 9)(x)

980 = 2x² + 9x

0 = 2x² + 9x - 980

0 = (2x + 49)(x - 20)

 

2x + 49 = 0

2x = -49

x = -24.5

 

x - 20 = 0

x = 20

 

Distance cannot be negative, so x has to equal 20 yards.

 

Plug the value into the length expression.

 

2x + 9 

2(20) + 9

49

 

The length is 49 yards.