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.

GAMEMASTERX40
Apr 7, 2018

edited by
GAMEMASTERX40
Apr 7, 2018

edited by GAMEMASTERX40 Apr 7, 2018

edited by GAMEMASTERX40 Apr 7, 2018

edited by GAMEMASTERX40 Apr 7, 2018

edited by GAMEMASTERX40 Apr 7, 2018

#1**+1 **

What are the dimensions of the rectangles? 18 ft x ? ft (can't read the depth on RHS).

Guest Apr 7, 2018

#2**+2 **

Sorry, the pic was blurry. The dimensions of the rectangle are 16 ft and 8 ft.

GAMEMASTERX40
Apr 7, 2018

#3**+3 **

area of stone path in sq ft = 16x + 8x - x^{2}

area of stone path in sq ft = 24x - x^{2} Plug in 80 for the area of the stone path.

80 = 24x - x^{2} Add x^{2} to both sides of the equation

x^{2} + 80 = 24x Subtract 24x from both sides.

x^{2} - 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

hectictar
Apr 7, 2018