Question

The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible value for the width?

40 cm
19.2 cm
16 cm
8 cm

Answer 1

The length of a rectangle is 5 times its width. Therefore, we can let the variable x represent the width of the rectangle and the term 5x represent the length.

We know that the perimeter of a rectangle can be found by adding twice the width to twice the length and we are told that the perimeter can't be more than 96 centimeters.

2W + 2L = P

2W + 2L ≤ 96

Now, we can substitute in our terms and simplify.

2(x) + 2(5x) ≤ 96

2x + 10x ≤ 96

12x ≤ 96 

x ≤ 8

We know that the width is equal to x, thus, the width cannot be more than 8 centimeters.

Hope this helps! :)

Answer 2

Here is the answer to the given problem above. Given that the width is x, and the length is 5x, the perimeter is 96. The formula for getting the perimeter is 2L + 2w =P. So let us solve for x. 2 (5x) + 2 (x) = 96
10 x + 2x = 96
12x = 96
x =8
Therefore, the width of the rectangle is 8cm. 
The answer for this would be the last option. 8cm is the greatest possible value of the width. Hope this helps.