Question

raul’s hamster’s house sits in the corner of its cage as shown in the diagram. the area around the house is 5 inches wide. write a simplified expression that represents the area around the house.
←5 in. 3x in.→
8 in.
5 in.

Explanation:

Step1: Find total length and width

Total length: \(5 + 3x\) inches. Total width: \(8 + 5 = 13\) inches.

Step2: Area of cage (total)

Area of cage: \((5 + 3x) \times 13 = 65 + 39x\) square inches.

Step3: Area of house

Area of house: \(8 \times 3x = 24x\) square inches.

Step4: Area around house

Subtract house area from cage area: \((65 + 39x) - 24x = 65 + 15x\) square inches.

Answer:

\(15x + 65\)