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In the given figure $DE | | BC$ . Find the value of $x$ .

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5

7

3

7 cm

answer is B.

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Detailed Solution

Given DE||BC and the figure is,
Question Image

Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
In

if a line DE is parallel to BC intersects AB at

and AC at

i.e.,

E | | BC

, then,

\frac{AD}{BD} = \frac{AE}{CE}

……….(1)
Now, from figure,

A D = x + 4, B D = x + 3 A E = 2 x − 1, C E = x + 1

Calculating the value of x from equation (1),

A D B D = A E C E ⇒ x + 4 x + 3 = 2 x − 1 x + 1 ⇒ x 2 + 4 x + x + 4 = 2 x 2 − x + 6 x − 3 ⇒ x 2 − 7 = 0 ⇒ x 2 = 7 ⇒ x = 7 cm

Thus, the required value of x is

7

cm.
Hence, the correct option is 2.

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