Question
Rectangle A is a scaled version of rectangle B. The dimensions of rectangle A are three times the dimensions of rectangle B. The area of rectangle B is 32 sq cm.
What is the area of rectangle A?
A.
96 sq cm
B.
16 sq cm
C.
288 sq cm
D.
144 sq cm
What is the area of rectangle A?
A.
96 sq cm
B.
16 sq cm
C.
288 sq cm
D.
144 sq cm
Answers
GPT-4o mini
To find the area of rectangle A, we start with the information provided:
1. The area of rectangle B is 32 sq cm.
2. The dimensions of rectangle A are three times the dimensions of rectangle B.
Since area is proportional to the square of the dimensions, if the dimensions of rectangle A are three times those of rectangle B, the area of rectangle A can be calculated as follows:
Area of rectangle A = (3 × Length of rectangle B) × (3 × Width of rectangle B) = 3^2 × (Length of rectangle B × Width of rectangle B)
This simplifies to:
Area of rectangle A = 9 × Area of rectangle B
Now substituting the area of rectangle B:
Area of rectangle A = 9 × 32 sq cm = 288 sq cm
Therefore, the area of rectangle A is **288 sq cm**.
The correct answer is **C. 288 sq cm**.
1. The area of rectangle B is 32 sq cm.
2. The dimensions of rectangle A are three times the dimensions of rectangle B.
Since area is proportional to the square of the dimensions, if the dimensions of rectangle A are three times those of rectangle B, the area of rectangle A can be calculated as follows:
Area of rectangle A = (3 × Length of rectangle B) × (3 × Width of rectangle B) = 3^2 × (Length of rectangle B × Width of rectangle B)
This simplifies to:
Area of rectangle A = 9 × Area of rectangle B
Now substituting the area of rectangle B:
Area of rectangle A = 9 × 32 sq cm = 288 sq cm
Therefore, the area of rectangle A is **288 sq cm**.
The correct answer is **C. 288 sq cm**.