Question

in the given figure,AM:MC = 3:4,BP:PM=3:2and BN=12 cm .

Find AN​

Answer 1

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Answer 2

AN = 14 cm

Step-by-step explanation:

Given:

AM : MC = 3 : 4, BP : PM = 3 : 2 and BN = 12 cm.

To find:

AN = ?

Construction:

Draw a line from point 'M' as parallel to CN and intersect line AB at 'R',

So  CN║MR.

Solution:

Let us take BMR

By construction, PN║MR  

By binomial proportionality theorem, we have

$\frac{BN}{NR} =\frac{BP}{PN}$

$\frac{12}{NR} =\frac{3}{2}$                      [given]

$NR=\frac{12\times 2}{3}$

NR = 8 cm

Let us take ANC,

By construction, RM║NC

By binomial proportionality theorem, we have

$\frac{AR}{RN} =\frac{AM}{MC}$

$\frac{AR}{8} =\frac{3}{4}$                             [given]

$AR=\frac{3\times 8}{4}$

AR = 6 cm

Now,

AN = AR + NR

AN = 8 + 6

AN = 14 cm