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