Luke and Seth each need to buy the same amount of fencing for their gardens. While Seth's garden is square in shape, Luke's garden is rectangular with the length 3 feet longer than Seth's. Luke's width is half of the length of his own garden. How much fencing did each buy?

6 feet

Step-by-step explanation:

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)

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