In a ΔABC, a line DE is drawn parallel to the side BC. If it is g

In a ΔABC, a line DE is drawn parallel to the side BC. If it is g
| In a ΔABC, a line DE is drawn parallel to the side BC. If it is given that AD : DB = 5 : 7, and AC = 15 cm, then find the length of AE?

A. 6 cm

B. 6.5 cm

C. 6.25 cm

D. 7 cm

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

GIVEN:

AD : DB = 5 : 7, and AC = 15 cm

CONCEPT:

For two similar ΔABC and ΔXYZ:

AB/XY = BC/YZ = AC/XZ

CALCULATION:

As DE is parallel to BC:

△ABC and △ADE will be similar (By AAA property)

So,

AD/AB = AE/AC

⇒ 5/(5 + 7) = AE/15

⇒ AE = 75/12

⇒ AE = 6.25 cm

∴ Length of AE is 6.25 cm

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