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Basic Proportionality Theorem

In the figure...

Question

In the figure given, if $D E ∥ B C$ and $A B = 5 x - 4, B D = 7 x - 5, C E = 5 x - 3$ and $A D = 3 x - 2$ , find the value of $x$ .

A

8

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B

1

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C

\frac{7}{10}

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D

\frac{9}{10}

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Solution

The correct option is B $1$
As $D E | | B C$ , $∠ A D E = ∠ A E D$
Here $△ A D E$ will be similar to $△ A B C$ .
Thus $\frac{A D}{A B} = \frac{A E}{A C}$
$\Rightarrow \frac{3 x - 2}{10 x - 7} = \frac{5 x - 4}{10 x - 7}$
$\Rightarrow 3 x - 2 = 5 x - 4$
$\Rightarrow - 2 + 4 = 5 x - 3 x$
$\Rightarrow x = 1$

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Similar questions

Q. In the figure if

D E ∥ B C

A D = 3 x - 2

A E = 5 x - 4

B D = 7 X - 4

B D - 7 x - 5

C E = 5 x - 3

Q. In the figure shown

D E ∥ B C

A D = 3 x - 2, A E = 5 x - 4, B D = 7 x - 5

C E = 5 x - 3

. Therefore, the value of

x

△

∥

A D = 4 x - 3

A E = 8 x - 7

B D = 3 x - 1

C E = 5 x - 3

then the value of

x

△

ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD =

4 x - 3

3 x - 1

8 x - 7

5 x - 3

x

Δ A B C

D

E

are points on the sides

A B

A C

respectively such that

D E | | B C

A D = 4 x - 3, A E = 8 x - 7, B D = 3 x - 1

C E = 5 x - 3

, find the value of

x

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