Q13 of 186 Page 253

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

Given that AB = 30cm and AD = 16 cm

∵ ∠ A = 90°

∴ ΔADB is a right-angled triangle.

Applying Pythagoras theorem,

BD² = BA² + AD²

⇒ BD ² = 30² + 16²

⇒ BD² = 900 + 256 = 1156

⇒ BD = 34 cm

∵ Diagonals of a rectangle are equal

∴ AC = 34 cm

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

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

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

In ΔABC, D is the midpoint of BC and AE ⊥ BC. If AC > AB, show that

AB² = AD² — BC • DE + 1/4 BC²