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In the given figure, MN||AB,BC=7.5cm, AM...

In the given figure, `MN`||`AB,BC=7.5cm, AM=4cm and MC=2 cm`. Find the length of BN.

A

`5` cm

B

`4`cm

C

`6`cm

D

`9`cm

Text Solution

Verified by Experts

The correct Answer is:
A
In `Delta ABC, MN||AB`.
`:. (MC)/(AC)=(NC)/(BC)`
`rArr (MC)/(AC=(NC)/(BC) " "` [ by Thales' therome]
`rArr (MC)/(AM+MC)=(NC)/(BC)`
`rArr (2)/(4+2)=(x)/(7.5), "where" NC=xcm`
`rArr x=(2xx7.5)/(6)=(15)/(6)=2.5`
`rAr NC=2.5cm`
Hence, `BN=BC-NC=(7.5-2.5) cm=5cm`
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