Word Problem: Do you know swimming pool designs?
Swimming pool design.
An architect has designed a motel pool within a rectangular area that is fenced on three sides as shown in the figure.
If she uses 60 yards of fencing to enclose an area of 352 square yards, then what are the dimensions marked L and W in the figure?
Assume that L is greater than W.
(Find exact and approximate solutions)
Comments
You don't give the figure so I will have to guess on a formula for the perimeter
P = L + 2W = 60
A = LW = 352
L = 352/W
352/W + 2W = 60
352 + 2W² = 60W
2W² - 60W + 352 = 0
W² - 30W + 176 = 0
W = [ 30 ± √(30² - 4(1)(176) ]/2
W = 15 ± √(900 - 704)/2
W = 15 ± √(196)/2
W = 15 ± √(196/4)
W = 15 ± √(49)
W = 15 ± 7
W = 22, 8
L = 352/W
L = 16 or 44
so one choice is W = 22, L = 16
the other is W = 8, L = 44