Question

A rectangular vegetable garden is to be 12 ft longer than it is wide. If you have at least 128 ft of fencing, what is the least measure that can be used for the width of the garden?

Answer 1

Answer:  26

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Work Shown:

w = width

12+w = length, because it's 12 ft longer compared to the width.

P = perimeter of rectangle

P = 2*(length + width)

P = 2*(12+w + w)

P = 2(2w+12)

P = 4w+24

The perimeter 4w+24 must be 128 or larger

$P \ge 128\\\\4w+24 \ge 128\\\\4w \ge 104\\\\w \ge 104/4\\\\w \ge 26$

Therefore, the width must be 26 feet or longer.

The smallest value you can use is w = 26

If w = 26 is the width, then 12+w = 12+26 = 38 is the length

P = 2*(L+W) = 2*(38+26) = 2*(64) = 128 is the perimeter

This helps confirm the answer.