Q12 of 186 Page 253

Find the height of an equilateral triangle of side 12 cm.

Δ ABC is an equilateral triangle.

Also, BC = AB = AC = 12 cm

The AD is the altitude at BC. Therefore, D is the midpoint of BC.

Now, ΔADB and ΔADC are right-angled triangles.

Applying Pythagoras theorem,

AB² = BD² + AD²

⇒ (12) ² = 6² + AD²

⇒ AD² = 144 – 36 = 108

⇒ AD = 6√3 cm

Find the length of altitude AD of an isosceles ΔABC in which AB = AC = 2a units and BC = a units.

ΔABC is an equilateral triangle of side 2a units. Find each of its altitudes.

Find the length of a diagonal of a rectangle whose adjacent sides are 30 cm and 16 cm.

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