CBSE Class 10 Maths Question Paper 2018 | Q17A

Question 17A: Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonals.

Video Explanation

Explanatory Answer | CBSE 2018 Maths Paper Q17A

Let ABCD be the square of side ‘a’ units.
Diagonal BD = \\sqrt{a^2 + a^2}\\) = \\sqrt2) a

The side of the first equilateral triangle is the same as the side of the square = a.
The side of the second equilateral triangle is the same as the diagonal of the square = √2 a
∴ Ratio of their side is a : √2 a = 1 : √2

Theorem: Ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.
Ratio of their areas = 1 : (√2)² = 1 : 2