how do you get 15 square units to make a perimeter 16 units?


Hello there.

Any flat shape can have an area and a perimeter. For example, a circle's perimeter is usually called a circumference. Irregular shapes also have perimeters, which is just the distance around the outside of the shape.

So you will need to be more clear about the shape you are trying to figure out.

If I assume that the shape you want is a rectangle, then this is how to solve it:

The area of a rectangle is length times width. Let's call that L x W.
The perimeter of a rectangle is L + L + W + W = 2L + 2W.

Now let's write these out with the values you've given and solve for L
in terms of W:

L x W = 15.

2L + 2W = 16 so L + W = 8.

At this point you may be able to use your number sense to complete the problem. Do you know two numbers with their product 15 and their sum 8?

If not, you can use algebraic methods.

L x W = 15 so L = 15 / W.

2L + 2W = 16 so L + W = 8 and thus L = 8 - W

But we now that if two different things equal the same third thing,
then they must equal each other, so

15 / W = 8 - W

Now if you solve for W, you will get two different numbers. Because
we weren't specific about whether the length or the width is shorter,
you can just choose one to be the width and the other is the length.
Remember to check your work by calculating the area and perimeter of a
rectangle with those dimensions.

Hope this helps,
Stephen and Penny.