Question

Find the area of the triangle with sides 21 cm, 16 cm and 13 cm. Also, find the perimeter of an equilateral
triangle equal in area to this triangle.​

Answer 1

Answer:\underline{\mathfrak{\huge{Question:}}}

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

\underline{\mathfrak{\huge{Answer:}}}

For this question, first we'll find the area of the other triangle with sides 21 cm, 16 cm and 13 cm :-

For this, we'll use the Heron's Formula :-

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

s = Semiperimeter

=》 s = \frac{P}{2}\\

=》 s = \frac{21 + 16 + 13}{2}\\

=》 s = 25 cm

Area of the triangle = \tt{\sqrt{25(25-21)(25-16)(25-13)}}

=》 Area = \tt{60\sqrt{3}}

We know that :-

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

=》 Area = 60\sqrt{3}

Keep them equal to each other and then solve them :-

=》 60\sqrt{3} = \frac{\sqrt{3}a^{2}}{4}\\

=》 60 = \frac{a^{2}}{4}\\

=》 \tt{a = 4\sqrt{15}}

Perimeter of the triangle = \tt{4\sqrt{15} + 4\sqrt{15} + 4\sqrt{15}}

=》 Perimeter =

Explanation: