Question

rag numbers to the lines to complete the expression that shows the area of the rectangle in terms of its width, w, in inches.
area = -1 w² + __ w + __
-52 -26 -13 0 1 13 26 52

Explanation:

Step1: Recall Rectangle Perimeter Formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is length and \( w \) is width. Given \( P = 52 \), we have \( 52 = 2(l + w) \). Dividing both sides by 2: \( 26 = l + w \), so \( l = 26 - w \).

Step2: Recall Rectangle Area Formula

The area \( A \) of a rectangle is \( A = l \times w \). Substitute \( l = 26 - w \) into the area formula: \( A = (26 - w)w \).

Step3: Expand the Expression

Expand \( (26 - w)w \): \( A = 26w - w^2 \), which can be rewritten as \( A = -1w^2 + 26w + 0 \).

Answer:

For the first blank (coefficient of \( w \)): \( 26 \)
For the second blank (constant term): \( 0 \)

So the completed expression is \( \text{Area} = -1w^2 + \boldsymbol{26}w + \boldsymbol{0} \)