Question

A rectangle has a length of 6x + 3 units and a width of 8 units.

Part A: Write a simplified expression for the area, in square units, of this rectangle.
Another rectangle has a length of 4x + 2 units and a width of 12 units.
Part B: Are the areas of both rectangles the same? Explain how you know.

Answer 1

Part A: 48x + 24 units^2

Part B: Yes; both rectangles have the same simplified expression for their area (48x + 24 units^2).

Explanation:

First you should know what the formula for finding the area of a rectangle is. The formula is: length (l) times width (w).

PART A:

Since you are given an expression for the length and the width, you can substitute these given values into the formula to form a simplified expression for Part A.

(length) * (width) ⇒ (6x + 3)(8)

Multiply to simplify this expression.

48x + 24 units^2 is the expression for the area of the rectangle.

PART B:

To find the answer for Part B, do the same thing you did for Part A. Substitute the values for length and width of this other rectangle into the formula.

(length) * (width) ⇒ (4x + 2)(12)

Multiply to simplify this expression.

48x + 24 units^2

This rectangle has the same expression as the other rectangle, so this means that they must have the same area.