Question

find the perimeter of an equilateral triangle whose area is equal to area of the triangle with sides 21cm 16cm 13cm.​

Answer 1

Answer:

12√15cm

Step-by-step explanation:

semi perimeter of ΔABC(s)= 21+16+13/2 =50/2= 25 cm

area= $\sqrt{s(s-a)(s-b)(s-c)}$

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

      =$\sqrt{25(4)(9)(12)}$

      =5×2×3×2√3

      =60√3cm²

area of equilateral Δ = ar(ΔABC)

=√3/4 a² =60√3

=a²=60×4

=a=√240

=a= 4√15cm

perimeter=3a=3×4√15

               =12√15 cm