Question

The width of a rectangle is 15 ft. shorter than its length. Its perimeter is 262 ft. Let l equal the length of the rectangle.

Answer 1

Let the length be l.
For now, let's make the width be w. 
Additionally, l = w + 15. Using this equation, width can also be written as l - 15. 
The perimeter of a rectangle is length + length + width + width. This can also be written as l + l + (l-15) + (l-15) = l + l + l - 15 + l - 15 = 4l - 30.
Using this equation:
4l - 30 = 262
4l = 292
l = 73

4(w + 15) - 30 = 262
4w + 60 - 30 = 262
4w + 30 = 262
4w = 232
w = 58