Question

Liam wants to build a rectangular pen for his new puppy. The length of the pen should be at least 10 ft, and the distance around should be no more than 30 ft. What is the system of inequalities that represents the possible dimensions of the pen?

Answer 1

Length is length, obviously. "The distance around" means "perimeter." Know the formula for the perimeter of a rectangle?

Answer 2

Once you have that formula, make an inequality out of it. Then graph the inequality.

Answer 3

I know the equation for perimeter, but I don't understand inequalities and graphing them.

Answer 4

@mathmale

Answer 5

Please type in the equation for the perimeter of a rectangle. Please name your variables and explain their meanings.

Answer 6

The problem states that "the distance around the rectangle must be no more than 30 ft."
So, the perimeter could have any value, up through and including 30 feet.

Answer 7

The equation for perimeter is 2(L+W).
Yes, I understand that.

Answer 8

Good. And the perimeter must be 30 or less ("no
more than 30"). Can you write that as an inequality?

Answer 9

Perimeter is less than or equal to 30

Answer 10

correct, and what is the formula for perimeter? You've already answered that question.

Answer 11

I still don't understand what the answer is. @mathmale

Answer 12

You've written: P = 2(L+W). Correct. this is the formula for the perimeter of a rect. of length L and width W.

The P must be 30 or less.

Therefore, you can write \[2(L+W)\le30\] and this can be simplified/ reduced. Do so, please.

Answer 13

Simply divide both sides of the inequality by 2. What do you get?

Answer 14

Your result must be another inequality.

Answer 15

I understand that the perimeter is 30 or less and the formula for perimeter, I don't understand how to divide both sides by 2.