Question

Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

Answer 1

We have,

ΔABC is an equilateral Δ with side 12 cm.

Draw AE ⊥ BC

In ΔABD and ΔACD

∠ADB = ∠ADC [Each 90°]

AB = AC [Each 12 cm]

AD = AD [Common]

Then, ΔABD ≅ ΔACD [By RHS condition]

∴ AD² + BD² = AB²

⇒ AD² + 6² = 12²

⇒ AD² = 144 − 36 = 108

⇒ AD = `sqrt(108)` = 10.39 cm