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

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
RELATED QUESTIONS
Jack used 54 ft of forming and 24 cubic ft of concrete to pour a sidewalk 4 inches thick. (answered by Theo)

A contractor is building a concrete sidewalk 10 ft. wide by 50 ft. long and 4 inches... (answered by ankor@dixie-net.com)

In Kendrick's dream home, he is now putting a sidewalk that goes from his driveway to his (answered by checkley79)

Carpentry: A carpenter needs to pour a rectangular slab 28 ft long, 16 ft wide, and 6 in... (answered by checkley71)

15. Carpentry: A carpenter needs to pour a rectangular slab 28 ft. long, 16 ft. wide,... (answered by bucky)

A garden is in the shape of a rectangle. One side of the garden has length 27 ft. The... (answered by richwmiller,josmiceli)

16. Construction: Concrete weighs 150 lb/cu ft. What is the weight of a concrete wall 18... (answered by MathLover1)

Construction: Concrete weighs 150 lb/cu ft. What is the weight of a concrete wall 18 (answered by waiwai933)

A contractor orders 8 cubic yards of premixed cement,all of which is to be used to pour a (answered by josgarithmetic,ikleyn,Theo)