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)
`w\geq 10` and
`2l+2w\leq 72`

B) w=8 l=28

C) w=11 l=39 does not work

Explanation:

An inequality is an equation that has a solution set or many possibilities for solutions. You write it with an inequality sign like
`\leq , \geq , < or >`.

A) The width must be at least 10 which means it must be equal o 10 or greater.

`w\geq 10`

The perimeter has the formula for a rectangle of 2l+2w=P. If the perimeter is no more than 72, then it is equal to 72 or less than it.

`2l+2w\leq 72`

B) The width could be 8 and the length could be 28 since 2*8+2*28 = 72

C) The width cannot be 11 and the length 39 cince 2*11 + 2*29 = 100.