A rectangular patio has an area of 91 ft 2 . The length is 6 feet longer than the width. Find the dimensions of the patio area. Solve by completing the square.

Question

Find the width and the length in terms of w

 

write an equation for the total area

 

find (b/2)^2

 

Find the dimensions

Answer 1

(6+W)W = 91

W^2 + 6W = 91

W^2 + 6W + 9 = 91+9 = 100

(W+3)^2 = 10^2

W+3 = 10 or -10

W = 10-3 = 7 or -10-3 = -13

L = 7+6 = 13

dimensions are 7 by 13 feet

total area = A = LW = 13(7) = 91 ft^2