Question

The length of each side of an equilateral triangle having an area of 25 under root 3 cm square is

Answer 1

GIVEN:

• Area of an equilateral triangle = 25√3 cm²

TO FIND:

• What is the length of the triangle ?

SOLUTION:

Let the side of an equilateral triangle be 'a' cm

We know that the formula for finding the area of an equilateral triangle is:-

$\large{\underline{\boxed{\bf{\star \: AREA = \dfrac{\sqrt{3}}{4} \times (side)^2 \: \star}}}}$

According to question:-

On putting the given values in the formula, we get

$\rm{\hookrightarrow \dfrac{\sqrt{\cancel{3}}}{4} \times (a)^2 = 25 \sqrt{\cancel{3}}}$

$\rm{\hookrightarrow \dfrac{1}{4} \times a^2 = 25 }$

$\rm{\hookrightarrow a^2 = 25 \times 4 }$

$\rm{\hookrightarrow a^2 = 100 }$

$\rm{\hookrightarrow a = \sqrt{100} }$

$\bf{ a = 10 \: cm}$

• Side = a = 10 cm

❝ Hence, the length of each side of an equilateral triangle is 10 cm ❞

______________________

Answer 2

Given that ,

The area of equilateral triangle is 25√3 cm²

We know that ,

The area of equilateral triangle is given by

$\large \rm \fbox{Area = \frac{ \sqrt{3} }{4} {(side)}^{2} }$

Thus ,

$\sf \mapsto 25 \sqrt{3} = \frac{ \sqrt{3} }{2} {(side)}^{2} \\ \\ \sf \mapsto {(side)}^{2} = 100 \\ \\ \sf \mapsto side = 10 \: cm$

$\therefore \sf \underline{The \: side \: of \: equilateral \: triangle \: is \: 10 \: cm}$