Question

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A rectangle has a perimeter equal to 24. If we consider its width x, how could we talk about its length y in terms of x? What are possible values of x? What are possible values of y?

y=

width is=

length is=

Answer 1

We know that the perimeter of a rectangle is 2l+2w

24=2y+2x

Subtract 2x on both sides (we are isolating y)

24-2x=2y

Divide 2 on both sides

Therefore, y=12-x

Some possible values using this equation..

y=8

x=4

Hope this helped :)

Answer 2

If the width is x, we count x twice since there are two widths in a rectangle. The perimeter is: 24 = 2x + 2y.

That means that 2y = 24 - 2x

and

y = 12 - x

x obviously has to be greater than 0, but to make sure that y is not zero and positive, we look at the equation y = 12 - x to determine possible values of x. The greatest possible value of x is 11, so: 0 < x < 11.

If we look back at our equation: 24 = 2x + 2y, we see that we can write it as:

2x = 24 - 2y or

x = 12 - y

We can use the same explanation we used to find the possible values of x to find the possible values of y: 0 < y < 11

So, the three answers are:

y = 12 - x

width is: 0 < x < 11

length is: 0 < y < 11