Question

the area of the entire rectangle to the right is ( x(x + 5) ). find another expression for this area by finding the sum of the areas of the smaller rectangles.

Explanation:

Step1: Identify the two smaller rectangles

The large rectangle is divided into two smaller rectangles. One has dimensions \( x \) (width) and \( x \) (height), and the other has dimensions \( x \) (width) and \( 5 \) (height).

Step2: Calculate the area of each small rectangle

• Area of the first small rectangle (top one): \( \text{Area}_1 = x \times x = x^2 \)
• Area of the second small rectangle (bottom one): \( \text{Area}_2 = x \times 5 = 5x \)

Step3: Sum the areas of the two small rectangles

To find the area of the entire large rectangle, we add the areas of the two smaller rectangles: \( \text{Total Area} = \text{Area}_1 + \text{Area}_2 = x^2 + 5x \)

Answer:

\( x^2 + 5x \)