Question

In an equilateral triangle of side
$3 \sqrt{3}$
find the length of the altitude ?​

Answer 1

Answer:

Given:

Side of an equilateral ∆ABC= 3√3 cm.

AB= AC=BC = 3√3 cm

Let AD = h (Altitude)

BD = ½ BC( ALTITUDE BISECTS THE BASE)

BD= ½(3√3)= 3√3/2 cm

AB² = AD²+ BD²

(3√3)² = h² + (3√3/2)²

27 = h² + 27/4

h² = 27 - 27/4

h² = (27×4 -27)/4

h²= (108 -27)/4

h²= 81/4

h=√(81/4)

h= 9/2= 4.5 cm

h= 4.5 cm

Hence, the length of the altitude is 4.5 cm.

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