Question

Note: Picture is not drawn to scale.

Rectangle A is a scaled version of rectangle B. The dimensions of rectangle B are twice the dimensions of rectangle A. The area of rectangle A is 50 sq cm.

What is the area of rectangle B?
A.
200 sq cm
B.
100 sq cm
C.
25 sq cm
D.
150 sq cm

Answer 1

To find the area of rectangle B, we first need to understand the relationship between the dimensions of rectangles A and B.

Since rectangle B has dimensions that are twice those of rectangle A, we can express the dimensions of rectangle B in terms of the dimensions of rectangle A.

Let the dimensions of rectangle A be \( l \) (length) and \( w \) (width). The area of rectangle A is given as:

\[
\text{Area of A} = l \times w = 50 \text{ sq cm}
\]

The dimensions of rectangle B, being twice those of rectangle A, will be:

\[
\text{Length of B} = 2l
\]
\[
\text{Width of B} = 2w
\]

Now, we can find the area of rectangle B:

\[
\text{Area of B} = \text{Length of B} \times \text{Width of B} = (2l) \times (2w) = 4(l \times w)
\]

Since we know that \( l \times w = 50 \text{ sq cm} \), we can substitute:

\[
\text{Area of B} = 4 \times 50 = 200 \text{ sq cm}
\]

Thus, the area of rectangle B is:

**A. 200 sq cm**