Students in an environmental club are planning a garden with four rectangular plots of land separated by stone paths, as shown. The stone paths will have the same width.
16 ft x 8 ft
a. The students plan to cover 80 square feet of path with stone. Write and solve an equation to find the width of the paths.
b. In part (a) you used one solution of an equation to find your answer. Explain how you chose which solution to use.
What are the dimensions of the rectangles? 18 ft x ? ft (can't read the depth on RHS).
area of stone path in sq ft = 16x + 8x - x2
area of stone path in sq ft = 24x - x2 Plug in 80 for the area of the stone path.
80 = 24x - x2 Add x2 to both sides of the equation
x2 + 80 = 24x Subtract 24x from both sides.
x2 - 24x + 80 = 0 What two numbers add to -24 and multiply to 80 ? -20 and -4 .
(x - 20)(x - 4) = 0 Set each factor equal to 0 and solve for x .
x - 20 = 0 or x - 4 = 0
x = 20 or x = 4
The width of the paths must be less than the lengths of the sides of the big rectangle,
so x must be less than 16 , and x must be less than 8 .
Since 20 is too large for the width of the paths, the only solution is x = 4