Notes: Find the length of the side of equilateral triangle of area 10.2 m^2?

Thursday, July 17, 2014

We'll recall the following formula that gives the area of
a triangle:

A = side*side*sine of the angle
included/2

Since the lengths of the sides of an equilateral
triangle are equal, let the length of the side be x.

A =
$\displaystyle{{x}}^{{{2}}}$ * sin 60/2

10.2 = $\displaystyle{{x}}^{{{2}}}$ * $\displaystyle\sqrt{{{3}}}$
/4

40.8 = $\displaystyle\sqrt{{{3}}}$ $\displaystyle{{x}}^{{{2}}}$

x
= $\displaystyle\sqrt{{\frac{{40.8}}{\sqrt{{{3}}}}}}$ m

x = 4.853
m

Therefore, the requested length of the side
of equilateral triangle is x = 4.853 m.

Notes