Answer: 15 by 30 feet, area is 450 square feet
Explanation:
Let the length be l and the width be w.
The perimeter is l+2w (since one side is against the house)
We also know the area is lw.
Since
, the area is the same as
.
The zeros of this area function are 0 and 30, so the value for which it is maximized is halfway between these values - 15.
If w=15, then l=30.
Therefore, the area is 450 square feet.