CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 7
7. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
Solution:
Given: ABCD is a square, AEB is an equilateral triangle described on the side of the square, DBF is an equilateral triangle described on diagonal BD of square.
To Prove:
Proof: Any two equilateral triangles are similar because all angles are of 60 degrees.
Therefore, by AAA similarity criterion,
~
(1)
{The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides}
But, we have
{Diagonal of square is
times of its side} (2)
Putting equation (2) in equation (1), we get
= 2
Therefore, area of equilateral triangle described on one side os square is equal to half the area of the equilateral triangle described on one of its diagonals.
Hence Proved
Aalap says
Thanks , really helped 🙂
Jashan says
Thanks @Aalap.. keep visiting.