Question

In triangle ABC, DEIIBC and AB=9cm EC=10cm and AC=18cm. Find the value of AD​

Answer 1

Answer:

AD=8CM

Step-by-step explanation:

AC-EC=AE

18-10=8

AE is opposite to AD

:AD=8

Answer 2

Given:

In triangle ABC, DEIIBC and AB=9cm EC=10cm and AC=18cm. Find the value of AD​?

To find:

The value of AD

Solution:

We know that,

$\boxed{\bold{Thales\: Theorem}} :$ If a line is drawn parallel to one of the sides of a triangle then it divides the other two sides proportionally.

Based on the above theorem, we get

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

$\implies \frac{AD}{AB - AD} = \frac{AC - EC}{EC}$

on substituting AB = 9 cm, EC = 10 cm and AC = 18 cm, we get

$\implies \frac{AD}{9 - AD} = \frac{18 - 10}{10}$

$\implies \frac{AD}{9 - AD} = \frac{8}{10}$

$\implies \frac{AD}{9 - AD} = \frac{4}{5}$

$\implies 5AD = 4(9 - AD)$

$\implies 5AD = 36 - 4AD$

$\implies 5AD +4AD = 36$

$\implies 9AD = 36$

$\implies \bold{AD = 4\:cm}$

Thus, the value of AD is → 4 cm.

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