Question

a rectangle is 8 feet long. its width is represented by \seven plus x feet.\ which expres represents the area, in square feet, of the rectangle?

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the formula \( A=\text{length}\times\text{width} \).

Step2: Identify the length and width

The length of the rectangle is 8 feet. The width is \( (7 + x) \) feet (since it is "seven plus \( x \) feet").

Step3: Substitute the length and width into the area formula

Substitute length \( = 8 \) and width \( = 7 + x \) into the formula \( A=\text{length}\times\text{width} \). So we have \( A = 8\times(7 + x) \).
Using the distributive property (also known as the distributive law of multiplication over addition), \( a\times(b + c)=a\times b+a\times c \), we can expand \( 8\times(7 + x) \) as \( 8\times7+8\times x \), which simplifies to \( 56 + 8x \) or \( 8x + 56 \).

Answer:

The expression representing the area of the rectangle is \( 8(7 + x) \) (or \( 8x + 56 \)) square feet.