The floor area of a COVID patient room is 160 square feet. If the length of the floor is four more than twice its width, then what are the dimensions of the floor of a patient’s room?

Question

a. Represent the length and the width using variable x.

b. Find the length and the width. Show a detailed flow of solution.

Answer 1

L = 4 + 2W

160 = LW = (4+2W)W = 4W + 2W^2

2W^2 + 4W - 160 = 0

divide by 2

W^2 + 2W - 80 = 0

(W+10)(W-8) = 0

W = 8, or -10 (ignore the negative solution)

W = 8 feet wide

L = 2W + 4 = 16 +4 = 20 feet long

Area = LW = 20(8) = 160 square feet

or if you're into using x, then let width = x = W

and length = L = 2x + 4

then area = LW = (2x+4)x = 2x^2 +4x = 160

you have a quadratic equation, solve for x by factoring, completing the square or use the quadratic formula

2x^2 +4x -160 = 0

x = -4/4 + or - (1/4)sqr(16 + 8(160))

x = -1 + 36/4 = 8 = width

2x+4 = 2(8)+4= 20 = length