Question

Natalia is drawing a rectangle. She wants the width to be at least 10 inches and the perimeter to be no more than 72 inches.

A.) write a system of inequalities that can be used to solve this problem.
B.) give a possible length and width for the rectangle.
C.) give a length and width that cannot be used for the rectangle.

Answer 1

A) Let's write equations with the given information. We will use L for length and W for width. Also, 2L+2W will represent the perimeter.

W >= 10
2L + 2W <= 72

B) To give a possible length and width, we don't need to solve the system. We can plug use numbers that will satisfy the equations above.

One possible solution would be W = 12 and L = 10. In this case, the width is greater than 10, and the perimeter is 44 which is less than 72.

C) One answer that would NOT work is W = 5 and L = 10 because width is less than 10.

Another example would be W = 20 and L = 18 because the perimeter would be greater than 72.