Mathematics

Mathematics

Problem

In

\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

. a. (i) Prove that

\triangle ADE \sim \triangle ABC

. b. (ii) Find the lengths

AD

and

AE

. c. (iii) Determine the ratio of the areas

[\triangle ADE] : [\triangle ABC]

. d. (iv) Hence find the area of

\triangle ADE

if

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

.

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