The area is 63

Question

The length of a rectangle is 5 feet more than twice the width. The area is 63 square feet. Find the length and width 

Answer 1

let say width is x

 

then the length is 2x +5

 

x(2x +5) = 63

 

2x^2 +5x = 63

 

2x^2 +5x -63 = 0

 

(2x - 9)(x + 7) = 0

 

x = 4.5 or -7

 

x must be positive value due to this is an area question.

 

so x = 4.5

 

width is 4.5 ft  and length is 14 ft

 

test the answer

 

4.5(2*4.5 + 5) = 4.5(14) = 63

 

Answer 2

L=5+2W (since the length is equal to twice the width (2W) and 5 feet)

A= L*W=(5+2W)*W=63

 

W(5+2W)=63

 

2W^2 +5W -63=0

(2W-9)(W+7)=0

 

either 2W-9=0 ---->W=9/2=4.5

or W+7=0 -------> W=-7

 

W can't be negative, therefore, W=4.5 feet

L=5+2W = 5+(4.5*2)=14feet

 

The solution is W=4.5 feet, L=14 Feet