determine the length and width

Question

a paper company makes a rectangle pieces of cardboard. the sheets have an area of 140 square inches. the length is 8 inches more than 3/5 its width. determine the length and width of the cardboard.

 

show all work alegrebraically

Answer 1

A = 140

A = LW

L = 8 + (3/5)W

 

140 = [8 + (3/5)W] W = 8W + (3/5)W^2

 

(3/5)W^2 + 8W - 140 = 0

 

Use quadratic formula:

 

W = {-8 ± sqrt[64 - 4(3/5)(-140)]} / (2*3/5) = (-8 ± 20) / (6/5)

 

Only positive square root gives positive W.

 

W = (20 - 8) * 5/6 = 10 inches

L = 8 + (3/5)(10) = 14 inches