Question

The triangles ABC and MNP are similar AB=12cm BC=8cm MN+NP=10 cm.Find the lenght of MN and MP ​

Answer 1

MN=6cm

NP= 4 cm

Explanation:

Step 1:

By the property of symmetry in triangle

`(BA)/(BC) =(MN)/(NP)`

By applying componendo and dividendo rule above equation is modified as

`(BA+BC)/(BA-BC) = (MN+NP)/(MN-NP)`

Step 2:

Applying the values in above equation

`(12+8)/(12-8) =(10)/(MN-NP)`

on simplification

MN-NP=
`(10*4)/(20)`

MN-NP=2

MN+NP=10

on solving above equations

2
`*`MN=12

MN=6 cm

NP=10-MN

=10-6

=4 cm