What is the length and width of a rectangle?

Question

Sydney made a rectangle using 24 square tiles. If she adds the length and width of her rectangle together she gets 11. What is the length and width of her rectangle?

Answer 1

Sydney, the area is L x W. To do this without Algebra, think of the factors of 24, add two of them together until you get 11. For example, we know 6 and 4 are factors, and 6+4 =10, so try another pair until you get 11.

Answer 2

Sydney,

 

We know that the length + width = 11, so L + W = 11 and we know that the area L x W = 24.

 

Set L = 11-W and substitute into the formula for area:  (11-W) x W = 24

 

⇒ 11W - W² = 24 or W² - 11W + 24 = 0

 

This factors to (W-8)(W-3) = 0

 

So we have W = 8 and W = 3 as solutions

 

Select W =3 as the width then L = 8.

 

Check:  these sum to 11 and their product is 24

Answer 3

Hi, Sydney. How do you visualize this problem? How have you attacked it so far? On this forum we can't just do your homework for you, but we can help you learn the ideas or help solve a problem when you get stuck. This one tells you the area of a rectangle: it's made of 24 square tiles. I think we have to add the assumption that each square tile measures 1 on each side. The problem should have said that, because we can't solve it without that assumption. So the area is 24 and the sum of the length and width is 11. What length and width make both of those things true?