If the area of a garen in 72 square feet, what are the dimensions of her garden. Keep in mind that the perimeter is 36.

OK......  We have

Area =L x W = 72     and Perimeter = 2(L + W) = 36

Working with the Perimeter and dividing by 2 on each side...... we have

(L + W ) = 18    Now, subtract W from both sides......we have

L = 18 - W       And substituting for L in the area equation, we have

(18- W) x W = 72    or   18W - W² = 72    ... Add  W² to both sides and subtract 18W from both sides

This gives       0 = W² - 18W + 72

And factoring the right side we have 0 = (W-6) (W-12)

And setting each factor to 0 we get W = 6 or W = 12

So, depending on your orientation, either [W = 6ft and  L = (18 - 6) =12ft] or [W = 12ft and L = (18 - 12) = 6ft]

Either way, the garden is 6ft by 12ft