Question

A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 270 square yards. Find the length and the width

Answer 1

L=W+3

A=LW, using L from above we get:

A=(W+3)W

A=W^2+3W, and we are told that A=270

W^2+3W=270

W^2+3W-270=0

W^2+18W-15W-270=0

W(W+18)-15(W+18)=0

(W-15)(W+18)=0 and W>0 so

W=15, and since L=W+3

L=18

So the width of the parking lot is 15 yards and its length is 18 yards.

Answer 2

3 yards greater than the width = w+3
where
width = w and length = L

However, since w+3 = L, we substitute w+3 for L.

Area of a rectangle: wL, or width x length.

Substitute: w x (w+3) = 270

Now, just solve.

We start by distributing the left side of the equation.

w(w+3) = w^2 + 3w = 270

Subtract 270 from both sides.

w^2 +3w - 270 = 0

We can't FOIL here, so back to good ol' quadratic formula.

Formula: (-b ± √(b²-4ac))/2a, where:

aw^2 + bw - c = 0

Thus:
a=1, b=3, c=-270.

Plug these values in for the variables in the equation, and you get two different values (depending on the plus/minus)

15 and -18.

However, distance(which is essentially the length of a certain line or how long something is) cannot be negative, so the only answer is 15.

Width is 15.

Plug into our original equation, 15 for w.

15L=270

Divide by 15 on both sides.

L = 18

Width: 15
Length: 18