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In $△ A B C$ , $D$ and $E$ are points on the sides $A B$ and $A C$ such that $D E ∥ B C$ . The lengths of $A D = 3.6 cm$ , $A B = 10 cm$ , $E C = 5.1 cm$ and AC will be,

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10cm

8.6cm

7.96cm

7cm

answer is C.

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Detailed Solution

Given that

and

are points on the sides AB and AC such that

D E ∥ B C

, the lengths of

A D = 3.6 cm

A B = 10 cm

and

E C = 5.1 cm

By Thale's theorem,

A D D B = A E E C

We have,

A D = 3.6 c m, A B = 10 c m, E C = 5.1 c m

A D D B = A E E C

⇒ A D A B − A D = A C − E C E C

…..i)
Substituting the values in equation i),

⇒ 3.6 10 − 3.6 = A C − 5.1 5.1 ⇒ 18.36 = 10 A C − 3.6 A C − 51 + 18.36 ⇒ 6.4 A C = 51 ⇒ A C = 7.96

Thus, the length of AC will be

7 . 96cm

.
Therefore the correct option is 3.

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