Question

A rectangular mat has a perimeter of 52 inches. Drag numbers to the lines to complete the expression that shows the area of the rectangle in terms of its width in inches.

Answer 1

To find the area of the rectangle in terms of its width, you need to express the length in terms of the width. Given that the dimensions of the larger square are twice the dimensions of the first square, you can replace the length with 2 times the width in the equation representing the perimeter of the rectangle. Solving the equation, you can find the width of the rectangle and then calculate the area using the formula A = width x length.

Step-by-step explanation:

The area of a rectangle can be found by multiplying its length and width. In this case, the perimeter of the rectangle is given as 52 inches, which can be expressed as 2 times the sum of the length and width. So, we have the equation 2(length + width) = 52.

To find the area in terms of the width, we need to express the length in terms of the width. Since the dimensions of the larger square are twice the dimensions of the first square, we can say that the length is 2 times the width.

Substituting this into the equation, we get 2(2w + w) = 52. Simplifying, we find that 6w = 52, which means that the width of the rectangle is 52/6 = 8.67 inches.

Therefore, the expression that shows the area of the rectangle in terms of its width is A = width x length = 8.67 x (2 x 8.67) = 150.35 square inches.

Answer 2

The expression for the area of the rectangle in terms of its width
`(\(w\))` is
`\(A = 26w - w^2\)`.

Let's find the expression for the area of the rectangle in terms of its width
`(\(w\))`.

1. The perimeter of a rectangle is given by
`\(P = 2l + 2w\)`, where
`\(l\)` is the length and
`\(w\)` is the width. In this case, the perimeter is given as 52 inches:

`\[52 = 2l + 2w\]`

2. Solve the perimeter equation :

`\[2l = 52 - 2w\]`

`\[l = 26 - w\]`

3. Substitute this expression for
`\(l\)` into the formula for the area
`\(A = l * w\)`:

`\[A = (26 - w) * w\]`

Now, let's simplify this expression:

`\[A = 26w - w^2\]`

Complete the question:

A rectangular mat has a perimeter of 52 inches. Drag numbers to the lines to complete the expression that shows the area of the rectangle in terms of its width, w, in inches.. Area = __w^2+ w+ _ _ _