The perimeter of rectangle Z is equal to its area.Rectangle Y has the same perimeter as rectangle Z.The length of rectangle Y is 5 inches and width of rectangle Z.

Two rectangles have a perimeter of 16 inches.Name one possible area for each rectangle.

To find the width of rectangle Z, let's first understand the information given.

We are told that the perimeter of rectangle Z is equal to its area. The perimeter of a rectangle is calculated by adding the lengths of all four sides.

Let's assign variables:

- Let Lz represent the length of rectangle Z.
- Let Wz represent the width of rectangle Z.

According to the given information, the perimeter of rectangle Z is equal to its area. The area of a rectangle is calculated by multiplying its length and width. Therefore, we can write the equation:

Perimeter of Z = 2(Lz + Wz)
Area of Z = Lz * Wz

To clarify, let's write down the equations using the given information again:

2(Lz + Wz) = Lz * Wz (equation 1)

Now, we are also given that rectangle Y has the same perimeter as rectangle Z. The length of rectangle Y is 5 inches, and we need to find the width of rectangle Z.

Let's assign variables for rectangle Y as well:

- Let Ly represent the length of rectangle Y.
- Let Wy represent the width of rectangle Y.

We know that rectangle Y has the same perimeter as rectangle Z. Writing this as an equation:

2(Ly + Wy) = 2(Lz + Wz) (equation 2)

Now, let's substitute the given values into equation 2:

2(5 + Wy) = 2(Lz + Wz)

Let's simplify equation 2:

10 + 2Wy = 2Lz + 2Wz

Since we want to find the width of rectangle Z, we can rearrange equation 2:

2Wz = 10 + 2Wy - 2Lz

Now, we can rearrange the equation to solve for Wz:

Wz = (10 + 2Wy - 2Lz) / 2

Plugging in the given values, where Ly = 5:

Wz = (10 + 2 * 5 - 2Lz) / 2

Simplifying further:

Wz = (10 + 10 - 2Lz) / 2

Wz = (20 - 2Lz) / 2

Wz = 10 - Lz

Therefore, the width of rectangle Z is given by the equation Wz = 10 - Lz.