The area of a rectangle is 28 ft2 , and the length of the rectangle is 1 ft more than double the width. Find the dimensions of the rectangle

Question

The area of a rectangle is 28 ft2 , and the length of the rectangle is 1 ft more than double the width. Find the dimensions of the rectangle

Answer 1

Area = 28 sqft = wl

w = width of rectangle

l = length of rectangle

l= 2w + 1

 

28 sqft = (w)ft (2w + 1) ft

28 = 2w^2 + w

 

0 = 2w^2 + w - 28

0 = (2w - 7)(w + 4)

so, w = 7/2 or w = -4

 

the width of the rectangle is a physical quantity that cannot be less than zero, so w= 7/2   or 3 1/2 is the answer.

 

double check the work by substituting 7/2 for w

28 = (7/2) [2(7/2) +1]

28 = (7/2)(7 + 1)

28 = (7/2)(8) = (7)(4)

 

which checks out.