Question

Note: Picture is not drawn to scale.

Triangle A is a scaled version of triangle B. The dimensions of triangle A are twice the dimensions of triangle B. The area of triangle A is 98 sq cm.

What is the area of triangle B?
A.
294 sq cm
B.
49 sq cm
C.
343 sq cm
D.
24.5 sq cm

Answer 1

To find the area of triangle B, we can use the property that when a shape is scaled by a factor, its area is scaled by the square of that factor.

In this case, triangle A is a scaled version of triangle B, and its dimensions are twice those of triangle B, meaning the scale factor is 2. The area scaling factor is the square of the linear scaling factor:

\[
\text{Area scaling factor} = (\text{scale factor})^2 = 2^2 = 4.
\]

Given that the area of triangle A is 98 sq cm, we can find the area of triangle B by dividing the area of triangle A by the area scaling factor:

\[
\text{Area of triangle B} = \frac{\text{Area of triangle A}}{\text{Area scaling factor}} = \frac{98 \, \text{sq cm}}{4} = 24.5 \, \text{sq cm}.
\]

Thus, the area of triangle B is:

\[
\boxed{24.5 \, \text{sq cm}}.
\]