word problems in algebra

Question

A farmer plans to use 180 feet of fencing to enclose a rectangular region, using part of a straight river bank instead of fencing as one side of the rectangle, as shown in the figure.

(a) Find the area A of the region if the length of the side parallel to the river bank is four times the length of an adjacent side.

A =  ft²

(b) Find the area A of the region if the length of the side parallel to the river bank is one-fourth the length of an adjacent side.

A =  ft²

(c) Find the area A of the region if the length of the side parallel to the river bank is the same as the length of an adjacent side.

A =  ft²

Answer 1

L=4W

L+2W= 180

4W + 2W = 180

6W = 180

W = 180/6 = 30 feet Wide

L=4W = 4(30)= 120 feet Long

Area = LW = 120(30)= 3,600 square feet

part b

if L=W/4

then LW = WW/4 = W^2/4 = Area

L+ 2W = 180

W/4 + 2W = 180

(9/4) W = 180

W = 4/9 of 180 = 80 feet Wide

L=W/4 = 80/4 = 20 feet Long

Area = LW = 80x20 = 1,600 square feet

part c

L=W

3W = 180

W = 60 feet = L

Area = LW = 60^2 = 3600