Question

2
dbe is obtained by enlarging abc. if the area of abc is 3 square units, what is the area of dbe?
ba = 2
bd = 6
a. 27 square units
b. 24 square units
c. 12 square units
d. 9 square units

Explanation:

Step1: Find scale factor of enlargement

The scale factor $k$ is the ratio of corresponding side lengths:
$k = \frac{BD}{BA} = \frac{6}{2} = 3$

Step2: Relate areas to scale factor

For similar figures, the ratio of areas is $k^2$. Let $A_{ABC}=3$, $A_{DBE}=A$.
$A = A_{ABC} \times k^2$

Step3: Calculate area of DBE

Substitute values:
$A = 3 \times 3^2 = 3 \times 9 = 27$

Answer:

A. 27 square units