word problem

Question

The length of a rectangle is 2
feet more than 3
times the width. If the area is 56
square feet, find the width and the length.

Answer 1

Hi Ramon.

 

Area of a rectangle is given by the formula

 

A = (length)x(width)

 

The length is 2 feet more than 3 times the width.

 

So use w for width, 

then length  will be 2 + 3w

 

The area is given as 56 sq ft

 

Plug all this into the formula and get that 

 

56 = (2+3w)x(w)

 

Distribute the w into the parentheses

 

56 = 2w + 3w²

 

Solve this by moving the 56 to the right side by subtracting it from both sides.

 

0 = 3w²+2w-56

 

This factors into (w-4)(3w+14)=0

 

So w = 4 or w=-(14/3)

 

Widths are usually positive, so lets check to see if w=4 satisfies the problem.

 

Length would be 2+3w or 2+3(4)=2+12=14

 

Does w=4 and length = 14 give area = 56?

 

A = lw = (14)(4) = 56   checks!  

 

So the width = 4 feet, the length = 14 feet.