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Basic Proportionality Theorem

In Δ ABC, ...

Question

In $Δ A B C$ , $D E I I B C$ , $A D = 2.5 c m$ , $D B = 5 c m$ , $A E = 3 c m$ and $E C = x c m$
Find the value of $x$ ?

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Solution

Solution:
$\frac{A D}{A D + B D} = \frac{A E}{A E + E C}$
$\frac{2.5}{7.5} = \frac{3}{3 + x}$
$3 + x = 9$
$x = 6$

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Similar questions

D and E are points on the sides AB and AC respectively of a $Δ A B C$ such that DE || BC
Find the value of x, when

(i) AD = x cm, DB = (x - 2) cm,

AE = (x + 2) cm and EC = (x - 1) cm.

(ii) AD = 4 cm, DB = (x - 4) cm, AE = 8 cm and EC = (3x - 19) cm.

(iii) AD = (7x - 4) cm, AE = (5x - 2) cm, DB = (3x + 4 ) cm and EC = 3x cm.

In the above figure ∆ABC~∆ADE. Given that AD=x cm, DB =x-3 cm, AE=4cm, EC=3 cm. What is the value of x?

D E ∥ B C

A D = x c m, D B = (x - 2) c m, A E = (x + 2) c m

E C = (x - 1) c m

x

∥

A D = 3 \cdot 6 c m, A B = 9 c m

A E = 2 \cdot 4 c m,

E C

\frac{A D}{D B} = \frac{3}{5}

A C = 5 \cdot 6 c m,

A E

A D = x c m, D B = (x - 2) c m, A E = (x + 2) c m

E C = (x - 1) c m,

x .

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