Question

Perimeter of a bigger triangle is 180 cm if the side of the smaller triangle is 8 cm 10 cm and 12 cm find the corresponding sides of the bigger Triangle

Answer 1

Answer:

Step-by-step explanation:step-by-step explanation: given: de is parallel to bc. de intersects ab and ac. to prove: ab/ad=ae/ec

construction: draw en perpendicular to ab and dm perpendicular to ac, join be and cd.

proof: ar(ade)=1/2 ad×en. (taking base ad)

ar(bde)=1/2 db×en.

this implies: ar(ade)/ar(bde)=1/2×ad×en/1/2db×en=ad/db (eq. 1)

ar(ade=1/2 ae*dm(taking ae base)

ar(dec)=1/2×ec×dm

this implies ar(ade)/ar(dec)=1/2 ae×dm=1/2 ec×dm=ae/ec. eq.2

ar(bde)=ar(dec(triangles on the same base and the same parallels are equal in area). eq.3

from equations 1, 2,3 we get: ad/db=ae/ec.

hence the theorem is proved.*

* this is a very important theorem in the chapter triangles class 10.