Question 6 Find the altitude of an equilateral triangle of side 8cm.
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Solution
Let ABC be an equilateral triangle of side 8 cm i.e., AB = BC = CA = 8 cm. Draw altitude AD which is perpendicular to BC. Then, D is the mid – point of BC.
∴BD=CD=12BC=82=4cm Now,AB2=AD2+BD2[byPythagorastheorem] ⇒(8)2=AD2+(4)2 ⇒64=AD2+16 ⇒AD2=64−16=48 ⇒AD=√48=4√3cm. Hence, altitude of an equilateral triangle is 4√3cm.