Question

Find the length of the side of an equilateral triangle if its area is given as
15.57 sq. cm. Also find the altitude of the triangle. (Take the value of 13 as 1.73)
Let the length of each side of the triangle be a cm.
Given: Area of the equilateral triangle = 15.57 sq. cm​

Answer 1

Given:-

• Area of the Equilateral Triangle = 15.57cm²

To Find:-

• Length of the side of an equilateral triangle.

• Altitude of the triangle

Formula Used:-

• ${\boxed{\bf{Area\:of\: Equilateral\: Triangle=\dfrac{\sqrt{3}}{4}a^2}}}$

• ${\boxed{\bf{Altitude\:of\: Equilateral\:Triangle=\dfrac{\sqrt{3}}{2}a}}}$

Solution:-

Firstly,

$\sf :\implies\:Area=\dfrac{\sqrt{3}}{4}a^2$

$\sf :\implies\:15.57=\dfrac{1.73}{4}a^2$

$\sf :\implies\:a^2=\dfrac{15.57\times4}{1.73}$

$\sf :\implies\:a^2=9\times4$

$\sf :\implies\:a=\sqrt{36}$

$\bf :\implies\:a=6\:cm$

Hence, The length of the side of Equilateral Triangle is 6cm.

Now,

$\sf :\implies\: Altitude=\dfrac{\sqrt{3}}{2}a$

$\sf :\implies\: Altitude=\dfrac{1.73}{2}\times6$

$\sf :\implies\: Altitude=1.73\times3$

$\bf :\implies\: Altitude=5.19\:cm$

Hence, The Altitude of the Equilateral triangle is 5.19cm.

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