how to find three dimensions of a total area

Question

A gardener wants to enclose a rectangular plot of land with 40 feet of fencing. The tomato plants are planted along a garage (so that is a natural barrier and needs no fencing), but the other three sides do. Find the three dimensions of the total area is 192 square feet.

Answer 1

Let x = width

Let y= length

Area = xy

Perimeter = x+x+y Plug in known values

192=xy

40=2x+y

This is 2 equations, 2 unknowns. It can be solved by substitution, as one possibility.

Solve for y in the second equation

y=40-2x Plug this into the area equation

192=x(40-2x) Distribute

192 = x(40-2x) Distribute

192 = 40x-2x² Add 2x² and subtract 40x from both sides

2x²-40x+192 = 0 Divide both sides by 2 to simplify

x²-20x+96 = 0 Factor

(x-12)(x-8)=0 Set equations equal to zero and solve

x=12 or x=8

Now find y for these solutions.

y=192/12

y=16

x=12

12+12+16=40

y=192/8

y=24

x=8

8+8+24 = 40