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प्रश्न
Find the altitude of an equilateral triangle of side 8 cm.
उत्तर
Let ABC be an equilateral triangle of side 8 cm
AB = BC = CA = 8 cm ...(All sides of an equilateral triangle is equal)
Draw altitude AD which is perpendicular to BC.
Then, D is the mid-point of BC.
∴ BD = CD = `1/2`
BC = `8/2` = 4 cm
Now, by Pythagoras theorem
AB2 = AD2 + BD2
⇒ (8)2 = AD2 + (4)2
⇒ 64 = AD2 + 16
⇒ AD = 64 – 16 = 48
⇒ AD = `sqrt(48)` = `4sqrt(3)` cm.
Hence, altitude of an equilateral triangle is `4sqrt(3)` cm.
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