In , and . Points and are taken on and respectively such that…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

\triangle ABC

AB = 12\,\text{cm}

and

AC = 18\,\text{cm}

. Points

D

and

E

are taken on

AB

and

AC

respectively such that

AD : AB = AE : AC = 2 : 5

. (i) Prove that

\triangle ADE \sim \triangle ABC

. (ii) Find the lengths

AD

and

AE

. (iii) Determine the ratio of the areas

[\triangle ADE] : [\triangle ABC]

. (iv) Hence find the area of

\triangle ADE

[\triangle ABC] = 270\,\text{cm}^2