algebra equation

Question

a client asked blake to design a rectangular garden with an area of 25 square feet. area of a rectangle is its length times its width. the client also requested that the length of the garden be seven feet less than two times the width. find the length and width of the garden. round your answers to three decimal places.

Answer 1

L=2W-7

LW =25

L=25/W

25/W = 2W-7 multiply both sides by W

25 =2W^2 -7W

2W^2 -7W -25 =0

use the quadratic formula

W = 7/4 + or - (1/4)sqr(49+200) = 5.6949 or 2.195

L = 2W-7 = 4.39 (ignore the 2.195 as it make L negative)

Width = slightly less than 5.695 feet

Length = 4.3898 = slightly less than 4.390 feet

5.695 x 4.390 = 25.001 square feet