SOLUTION: Sue used 54 ft of forming and 24 cubic ft of concrete to pour a sidewalk 4 inches thick. Assuming that the length is the larger of the dimensions, what was the length of the sidew
Algebra ->
Finance
-> SOLUTION: Sue used 54 ft of forming and 24 cubic ft of concrete to pour a sidewalk 4 inches thick. Assuming that the length is the larger of the dimensions, what was the length of the sidew
Log On
Question 1124149: Sue used 54 ft of forming and 24 cubic ft of concrete to pour a sidewalk 4 inches thick. Assuming that the length is the larger of the dimensions, what was the length of the sidewalk? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! used 54 ft of forming and 24 cubic ft of concrete to pour a sidewalk 4 inches thick.
Assuming that the length is the larger of the dimensions, what was the length of the sidewalk?
:
let L = the length of the side walk
let w = the width
The forming is the perimeter of the side walk
2L + 2w = 54
Simplify, divide by 2
L + w = 27
w = (-L+27), we can use this form for substitution
:
We can find area of the concrete by dividing by the depth, 4" which is ft
24 divided by 1/3 = 72 sq/ft
therefore the area equation
L*w = 72
replace w with (-L+27)
L(-L+27) = 72w
a quadratic equation
-L^2 + 27L - 72 = 0
Multiply equation by -1
L^2 - 27L + 72 = 0
Factors to
(L-3)(L-24) = 0
L = 24 ft is the length of sidewalk
:
;
Confirm this by finding the perimeter (forming). Width is 3 ft
2(24) + 2(3) = 54
