What are the dimensions of a rectangle with a perimeter of 401 feet and an area of 100 feet?

Answer 1

The rectangle cannot have an area of 100 feet, since that is a measure of distance and not area. Assume, therefore, that the area is 100 SQUARE feet.

Suppose the rectagle has length L and width W

then 2(L + W) = 401

and L*W = 100

So L = 100/W

Then 2(100/W + W) = 401

Multiply by W: 2(100 + W2) = 401W

or 2W2 - 401W + 200 = 0

or (2W - 1)(W-200) = 0

So W = 0.5 ft or W = 200 ft which imply that L = 200 ft or 0.5 ft respectively.

So, the dimensions are 200 ft by 0.5 ft (or 6 inches).