Q14 of 186 Page 274

In an equilateral triangle with side a, prove that area = .

Let ∆ ABC be an equilateral triangle with side a.

To prove: Area of ∆ ABC =

In ∆ ABC, AD bisects BC

Now, in ∆ ACD

Using Pythagoras theorem,

AC² = AD² + DC²

⇒ AD² = AC² – DC²

Now, in ∆ ABC

Area of ∆ ABC =

In the given figure, LM || CB and LN || CD. Prove that

Prove that the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.

Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.