Question

in the adjacent figure MN ||AB ,BC= 7.5 cm ,AM=4 cm and MC =2 cm find the length of the BN​

Answer 1

It is given that in ∆ABC , MN ।। AB.

And, BC = 7.5 cm , AM = 4cm & MC = 2cm.

So, by Thales Theorem,

AC/MA = BC/BN

(CM + MA) / MA = BC / BN

(2 + 4) / MA = BC / BN

6 / 4 = 7.5 / BN

BN = ( 7.5 x 4 ) / 6

BN = ( 75 x 4 ) / 60

BN = 300/60

BN = 5.

Hence, the length of BN is 5cm.

Answer 2

Answer:

BN = 5 cm.

Step-by-step explanation:

Given:- MN || AB, BC = 7.5 cm, AM = 4 cm, MC = 2cm.

To Find:- Length of BN

Solution:-

From the given figure, BC || NC.

∵ MN || AB

∴ ∠ABC = ∠MNC    (Corresponding angles)

Now in ΔABC and ΔMNC,  

∠ABC = ∠MNC      (Corresponding angles)  

∠ACB = ∠MCN      (Common angles)  

∠BAC = ∠NMC     (Corresponding angles)  

∴ ΔABC ≅ ΔMNC.      (BY AAA similarity criteria)  

∴ $\frac{AC}{MC}$ = $\frac{BC}{NC}$ (By property of similar triangles)

⇒ NC = $\frac{BC * MC}{AC}$

⇒ NC = $\frac{BC * MC}{AM + MC}$

⇒ NC = $\frac{7.5 * 2}{4 + 2}$

⇒ NC = $\frac{15}{6}$

⇒ NC = $\frac{5}{2}$ = 2.5 cm.

∵ BN = BC - NC

∴ BN = 7.5 - 2.5

        = 5 cm.

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