Question

A rectangle had a width thet is 12 more than half its length, l. write an expression for the perimeter, p of the rectangle, in terms of l.

Answer 1

p = 3l + 24

Explanation:

Finding an expression relating the width (w) and length (l):

Before we can find an expression for the rectangle's perimeter in terms l, we first need to find an expression that relates the width and length.

Since the width is 12 more than half the length, our expression is given by:

w = 1/2l + 12

• Now we can use this expression for w in our perimeter expression to completely eliminate the variable w.

Finding an expression for perimeter in terms of l:

The formula for the perimeter of a rectangle is given by:

p = 2l + 2w, where

• p is the perimeter,
• l is the length,
• and w is the width.

If we substitute 1/2l + 12 for w, our formula is given by:

p = 2l + 2(1/2l + 12)

p = 2l + l + 24

p = 3l + 24

Thus, p = 3l + 24 is an expression for perimeter in terms of l.