Question

The perimeter of a parallelogram must be no less than 40 feet. The length of the rectangle is 6 feet. What are the possible measurements of the width?

Write an inequality to represent this problem. Use w to represent the width of the parallelogram. [Hint: The formula for finding the perimeter of a parallelogram is \(P=2l+2w.\)
What is the smallest possible measurement of the width? Justify your answer by showing all your work.

Answer 1

12+2w>40

w > 19

A minimum value of w is 20ft.

Explanation:

If the variable l is the length of the parallelogram, and w is its width, then the perimeter of the parallelogram will be,

P = 2l + 2w.

l = 6ft and P > 40ft.

Thus, 2(6) + 2w > 40

-> 12 + 2w > 40

This is the required inequality.

Now, 2w > 38

-> w > 19ft.

So currently, the smallest possible measurement of the width is 20ft.

Explanation:

Answer 2

see below

Explanation:

If you know that your perimeter must be no less than 40 feet, you can say that P >= 40 ft. Since P is given by P=2l+2w, you can combine the two equations into a single inequality:

2l+2w >= 40

If the length is given by 6 feet, then you can further simplify the inequality to be

12+2w >= 40 --> w >=14

This means that the smallest possible measurement of the width is 14 feet.