Question

Given ΔABC, AB = BC = AC . Area of ΔABC = 25√3/4 cm. Find the perimeter of ΔABC.

Answer 1

ΔABC, AB = BC = AC
It's equilateral triangle
so
(√3)
A = --------a^2
4
25 (√3) (√3)
-------------- = --------a^2
4 4
a^2 = 25
a = 5

P = 3a = 3 x 5 = 15

answer
15 cm

Answer 2

Given ΔABC, AB = BC = AC . Area of ΔABC = 25√3/4 cm. Find the perimeter of ΔABC.
Answer: This is an equilateral triangle of height a√3/2 where a is the side length. So the area is ½a.a√3/2=a²√3/4.
So a²=25 and a=5cm. Therefore the perimeter is 3a=15cm.