Question

Find the length of the height of an equilateral triangle of side 24 cm.

Answer 1

Let us assume the height of an equilateral triangle be h cm.

Then,

Area of the triangle = (1/2) × base × height

= ((1/2) × 24 ×h) cm²

Let the side of the equilateral triangle be a cm

Area of the equilateral triangle = ((√3)/4) × (a)² sq. Units

= (((√3)/4) × 24 ×24)

= (√3 × 144) cm²

∴ ((1/2) × 24 ×h) = (√3 × 144)

= 12 h = (√3 × 144)

= h = (√3 × 144)/12

= h = (√3 × 12)

= h = 1.73 × 12

= h = 20.76 cm

Hence, the height of an equilateral triangle is 20.76 cm