Question

find the perimeter of an equilateral triangle whose area is equal to that of a triangle with sides 21 cm,16cm,and 13cm.

Answer 1

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Answer 2

The perimeter of equilateral is 46.77 cm

Step-by-step explanation:

Sides of triangle :

a = 21 cm

b = 16 cm

c = 13 cm

Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Where $s=\frac{a+b+c}{2}$

Substitute the values :

$s=\frac{21+16+13}{2}\\s=25$

Area = $\sqrt{25(25-21)(25-16)(25-13)}=103.923$

Area of equilateral triangle = $\frac{\sqrt{3}}{4}a^2$

So, $\frac{\sqrt{3}}{4}a^2=103.923\\a=15.59$

So,Perimeter of equilateral triangle = $3 \times side = 3 \times 15.59=46.77 cm$

Hence the perimeter of equilateral is 46.77 cm

#Learn more :

Find the perimeter of an equilateral triangle whose area is equal to that of a triangle with sides 21 cm,16cm,and 13cm

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