Math CentralQuandaries & Queries


Question from Peter, a student:

A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side?


This room has a small, rectangular closet with a perimeter of 18 feet and an area of 14 square feet. The perimeter is distance around the 4 sided so if the lengths of the sides are x feet and y feet then 2x + 2y = 18 so

x + y = 9 feet.

The area is 14 square feet so

xy = 14 square feet.

From the first equation

y = 9 - x

and if you substitute this into the second equation you get

x (9 - x) = 14
9x - x2 = 14
x2 - 9x + 14 = 0

This equation factors

(x - 7)(x - 2) = 0

Thus x = 7 or x = 2 feet and hence the closet is 7 feet by 2 feet. What are he dimensions of the room?


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS