Question

1. which of the following situations could be represented by the expression, x(x + 7)? a rectangle has a width seven times its length. write an expression, in terms of x, for the area of the rectangle. a rectangle has a width 7 inches longer than its length. write an expression, in terms of x, for the area of the rectangle. a rectangular prism has a width seven times longer than its height. its height and width are the same length. write an expression, in terms of x, for the surface area of the rectangular prism. a rectangular prism has a width 7 inches longer than its height. its height and width are the same length. write an expression, in terms of x, for the volume of the rectangular prism.

Explanation:

Step1: Analyze the form of the expression $x(x + 7)$

The expression $x(x + 7)=x\times(x + 7)$ is in the form of the area formula of a rectangle $A = l\times w$, where if we let the length of the rectangle be $x$ and the width be $x + 7$. The situation that a rectangle has a width seven times its length is not represented by $x(x + 7)$. A rectangle with width 7 inches longer than its length, if the length is $x$, the width is $x+7$ and the area is $x(x + 7)$.

Step2: Match the description with the expression

The description "A rectangle has a width 7 inches longer than its length. Its height and width are the same length. Write an expression, in terms of $x$, for the volume of the rectangular prism" is not relevant to $x(x + 7)$ as it is about volume of a 3 - D shape. Also, "A rectangular prism has a width seven times longer than its height. Its height and width are the same length. Write an expression, in terms of $x$, for the surface - area of the rectangular prism" is not relevant as it is about surface - area of a 3 - D shape. The correct situation for the expression $x(x + 7)$ is when a rectangle has a width 7 inches longer than its length and we are finding the area of the rectangle.

Answer:

A rectangle has a width 7 inches longer than its length. Write an expression, in terms of $x$, for the area of the rectangle.