the length of a rectangle is 9 inches less than twice the width. if the perimeter of the rectangle is 84 inches, find the dimensions of the rectangle.

translate each statement into mathematical language

length is nine inches less than twice width. L = 2W - 9

perimeter is 84 inches 2L + 2W = 84

Substitute the expression for L (2W-9) for L in the second equation resulting in the follwing

2 (2W-9) + 2W = 84

4W - 18 + 2W = 84

(4W+2W) = 84+18

6W = 102

W = 102/6 = 51/3

L = 2 (51/3) - 9

= L = 17-9

L=6