Question

given triangle abc, ab =bc=ac area of triangle abc 25 sq root 3 divide 4 cm. find the perimeter of abc tirangle

Answer 1

`\boxed{Circuit_(\Delta ABC) = 15~cm }`

Explanation:

The ABC triangle is an equilateral triangle.

`\mid AB\mid = \mid BC\mid = \mid AC\mid`

The drawing in the attachment.

I am entering meaningfully:

a - side length of an equilateral triangle

`a=\mid AB\mid = \mid BC\mid = \mid AC\mid`

`P_(\Delta) =(a^(2) √(3) )/(4)` - equilateral triangle area formula

`P_(\Delta) =(25 √(3) )/(4)~~\land~~P_(\Delta) =(a^(2) √(3) )/(4)~~\Rightarrow~~(a^(2) √(3) )/(4)=(25 √(3) )/(4)\\\\\\(a^(2) √(3) )/(4)=(25 √(3) )/(4)~~\mid~~/ ~~(√(3) )/(4) \\\\\\(a^(2) √(3) )/(4)\cdot (4)/(√(3) ) =(25 √(3) )/(4)\cdot (4)/(√(3) ) \\\\a^(2) =25~~\\\\a^(2) =5^(2) ~~\land~~a > 0~~\Rightarrow~~\boxed{a=5~cm}\\\\\\`

`Circuit_(\Delta ABC) =a+a+a\\\\Circuit_(\Delta ABC) =3a~~\land~~a=5~cm\\\\\boxed{Circuit_(\Delta ABC) =3\cdot 5 = 15~cm }`

The perimeter of the triangle ABC is 15.