The length of each side of an equilateral tri | vedclass

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Question

(B) An equilateral triangle has all sides equal. Given side $a = 12\, cm$.The formula for the height $h$ of an equilateral triangle is $h = \frac{\sqr

Vedclass · Accepted Answer

$6 \sqrt{3}\, cm$

Vedclass · Answer

(B) An equilateral triangle has all sides equal. Given side $a = 12\, cm$.The formula for the height $h$ of an equilateral triangle is $h = \frac{\sqrt{3}}{2} 	imes a$.Substituting the value of $a$:$h = \frac{\sqrt{3}}{2} 	imes 12\, cm$$h = 6 \sqrt{3}\, cm$.Alternatively,using the area formula:Area $= \frac{\sqrt{3}}{4} 	imes a^2 = \frac{\sqrt{3}}{4} 	imes 144 = 36 \sqrt{3}\, cm^2$.Also,Area $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 12 	imes h = 6h$.Equating the two: $6h = 36 \sqrt{3}$,so $h = 6 \sqrt{3}\, cm$.

The length of each side of an equilateral triangle is $12\, cm$. The height of the triangle is

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