ch. 5.7-5.8 homework

Question

The length of a rectangle is 5 feet more than 2 times the width. If the area is 52 square feet, find the width and the length.
width 

width ft= ?

 

length ft =?

Answer 1

1. Area = Length x Width = 52 sq ft

 

2. Length = 2 x Width +5

 

Substitute value of Length in equation 2 into equation 1 giving 

 

Area = 52 = (2 x Width +5) x Width

52=2Width² + 5Width or 

 

2Width² + 5Width - 52 = 0 which factors into (2Width + 13) and (Width -4) of Width = -13/2 and 4. Since a negative number is not possible for a measurement, the Width = 4

 and Length =  2 x Width +5 = 2 x 4 +5 = 13