The Mitchells are designing a garden. The garden will be in the shape of a rectangle and have an area of 270 square feet. The width of the garden is 3 feet less than the length. Find the width

Answer 1

let w = width = L-3 (3ft less than length)

 let L = length

 A=L*w

 A=L * (L-3)

 A = L² - 3L

 270 = L²  - 3L

 L²  - 3L - 270 = 0  

 now factor it:

 L² -18L +15L -270 = 0

(L+15)(L-18) = 0

 L= -15 or 18

 

L= 18   (the other factor will give a negative value so we can't take that)

 

w = L-3 = 18-3=15

 

so the A=Lw = 18*15 = 270 and it checks out

 

Hope this was helpful.

Answer 2

W=L-3

L=W+3

LW = 270

(W+3)W = 270

W^2 +3W = 270

W+3W + 9/4 = 270 + 9/4

(W+3/2)^2 = 1089/4

W+ 3/2 = (1/2)sqr1089

W = -3/2 + 33/2 = 30/2 = 15 feet wide

W=15 feet

L=18 feet

18x15=270