Multiple Choice Question (MCQ)
In the figure, if AE = 3, DE = 5, and CE = 7, then BF equals:

×
3.6

×
4.0

✓
4.2

×
4.5

×
5.0
In the figure, if AE = 3, DE = 5, and CE = 7, then BF equals:
3.6
4.0
4.2
4.5
5.0
\angle BAF and \angle DAE are complementary angles, which means their sum is 90\degree . Therefore, \triangle AED and \triangle BFA are similar. Similarly, \triangle CFB and \triangle DEC are also similar.
Therefore, we get the following equations.
Divide (1) by (2), we get
On the other hand,
Solve the system of equations (3) and (4),
We get, CF = 3 and AF = 7
Using the equation (2),
BF = \dfrac{7}{5}\times CF = \dfrac{7}{5}\times 3 = 4.2