A rectangular garden covers 44 yd2. The length is 3 yards less than twice the width.

Question

a. Clearly define the variable you will use AND draw a picture to illustrate the problem

b. Write an equation using ONE variable that you could solve to find the length and width of the garden

c. Solve your equation to from part b. to find the length and width of the garden Write your answer in a complete sentence.

Answer 1

LW= 44 = area = length times width

L=2W-3 Length is 3 less than twice width. L=length W=width

(2W-3)W=44 substitute formula for L into area equation

2W^2 - 3W -44 = 0 expand

use quadratic formula to solve for W

W= (3+ or - sqr(9-4(2)(-44))/4 = 3/4 + or - (1/4)sqr361 = 3/4 + or - 19/4 = 22/4 = 5.5 yards

ignore the 2nd solution as it gives a negative width and negative length

L=2W-3 = 2(5.5)-3 = 11-3 = 8 yards

8x5.5 yard garden 8x5.5=44,

The garden is 8 yards by 5 1/2 yards