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.

Write an expression for the width in terms of the length.

Write an equation for the perimeter in terms of l.

Solve the equation, clearly indicating the length of the rectangle.

Solve for the width of the rectangle. Clearly indicate the width 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