A = Lw (Area equal length times width)
A = 48 (the garden's area is 48 ft2)
L = w + 2
We have values for our variables, so let's plug them in:
48 = w(w + 2)
Distribute:
48 = w2 + 2w
Subtract 48 from both sides:
0 = w2 + 2w - 48
AS you can see, we now have a quadratic. From here we need:
m + n = 2 and
m * n = -48
When we break up the quadratic into (w + m)(w + n)
48 is an even number divisible by 3, so it'll be also be divisible by 6:
48 / 6 = 8
8 + (-6) = 2
8 * -6 = -48, so:
0 = (w + 8)(w - 6) →→ 0 = w + 8, or 0 = w - 6
w = -8 or 6
We can't have a negative width, so it cannot be -8, therefore, the width is 6 ft. I'm sure you can find the length from here.
(i hope this is right)
