MathematicsIn given figure, MN || QR. If PM=x cm, MQ=10 cm, PN=x-2 cm and NR=6 cm, then find the value of x.

In given figure, $MN | | QR$ . If $PM = x cm$ , $MQ = 10 cm$ , $PN = (x - 2) cm$ and $NR = 6 cm$ , then find the value of x.

A
11 cm
B
9 cm
C
10 cm
D
5 cm

Solution:

It is given that

MN | | QR

PM = x cm

MQ = 10 cm

PN = (x - 2) cm

and

NR = 6 cm

Basic proportionality theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
As it is given that

MN | | QR

so apply the basic proportionality theorem in

ΔPQR

.
Thus,

\frac{PM}{MQ} = \frac{PN}{NR}

\Rightarrow \frac{x}{10} = \frac{x - 2}{6}

Cross multiply the above equation.

6 x = 10 x - 20

\Rightarrow 4 x = 20

\Rightarrow x = 5 cm

Therefore, the value of x is 5 cm.
Hence, option 4 is correct.

In given figure, $MN | | QR$ . If $PM = x cm$ , $MQ = 10 cm$ , $PN = (x - 2) cm$ and $NR = 6 cm$ , then find the value of x.

Solution:

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