Question

In ∆ABC, seg DE || side BC. If DB = 8 cm, AD = 12 cm, EC = 10 cm then find AE and AC.​

Answer 1

Given:

In ∆ABC, seg DE || side BC. If DB = 8 cm, AD = 12 cm, EC = 10 cm then find AE and AC.​

To find:

AE and AC

Solution:

We know,

$\boxed{\bold{Basic\:Proportionality\:Theorem\: / \:Thales\:Theorem}} :$

The theorem states that if a line is drawn parallel to any one side of a triangle,  intersecting the other two sides at two distinct points, then the other two sides are divided in the same ratio.

Based on the above theorem, we get

$\frac{AD}{DB} = \frac{AE}{EC}$

on substituting DB = 8 cm, AD = 12 cm, EC = 10 cm, we get

$\implies \frac{12}{8} = \frac{AE}{10}$

$\implies AE = \frac{12\times 10}{8}$

$\implies \bold{AE = 15\:cm}$

∴ AC = AE + EC = 15 + 10 = 25 cm

Thus,

The length of AE is → 15 cm.

The length of AC is → 25 cm.

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