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Question
Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.
Solution
(1)The area of the equilateral triangle=`sqrt3/4xx"side"^2`
=`sqrt3/4xx10^2`
=`sqrt3/4xx100`
=`25sqrt3 cm^2`
or `25xx1.732=43.3cm^2`
So, the area of the triangle is `25sqrt3 cm^2 or 433cm^2`
(2) As, area of the equilateral triangle =`25sqrt3 cm^2`
⇒`1/2xx "Base" xx "Height"=25sqrt3`
⇒` 1/2xx10xx"Height"=25sqrt3`
⇒ `5xx"Height"=25sqrt3`
⇒`"Height" =(25sqrt3)/5=5sqrt3`
Or `"Height" = 5xx1.732=8.66m`
∴ The height of the triangle is `5sqrt3 cm or 8.66 cm`
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