1.

The perimeter of an equilateral triangle is 60 cm. Find its (i) area and (ii) height. (Given, `sqrt(3) = 1732`.)

Answer» Perimeter of the given equilateral triangle = 60 cm.
Length of each of its sides `=(60)/(3) cm = 20 cm`.
(i) Area of the triangle `=((sqrt(3))/(4)xx a^(2))`sq units
`=((sqrt(3))/(4)xx 20 xx 20)cm^(2)=(100 xx sqrt(3))cm^(2)`
`=(100 xx 1.732)cm^(2) = 173.2 cm^(2)`.
Hence, the area of the given triangle is 173.2 `cm^(2)`.
(ii) Let the height of the given triangle be h cm. Then,
`"its area"=((1)/(2)xx "base" xx "height")=((1)/(2)xx 20 xx h)cm^(2)`.
`therefore" "(1)/(2)xx 20 xx h=173.2 rArr h=(173.2)/(10) rArr "height" = 17.32 cm`.
Hence, the height of the given triangle is 17.32 cm.


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