Ex 6.4, 8 (Introduction)
Tick the correct answer and justify :
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4
Two equilateral triangle are always similar
In
= 12 6
= 12 6
= 12 6
Hence by SSS similarity
~
Ex 6.4, 8
Tick the correct answer and justify :
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
2 : 1 (B) 1 : 2 (C) 4 : 1 (D) 1 : 4
Given:
is equilateral
is equilateral
BD = 1/2 as D is midpoint of BC
To find: ( )/( )
Solution:
Since , and are equilateral,
Their sides would be in the same ratio
/ = / = /
Hence, by SSS similarity
~
And , we know that ratio of area of triangle is equal
To the ratio of square of corresponding sides
So, ( )/( )=( )^2/( )2
=( )^2/( /2)^2
= 2/(( ^2)/4)
=4 2/ 2
= 4/1
Hence, ( )/( )=4/1 i.e. 4 : 1
Option (C) is correct

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.