Question

A square and an equilateral triangle have the same perimeter. If the diagonal of the square is 12√5 cm, then find the altitude of equilateral triangle.

Answer 1

let side of the square be a cm
so, a√2 = 12√5
so a = 12√5/√2
4a = 48√5/√2
4a is the perimeter of the square as well as the triangle
so side of the equilateral triangle = 4a/3 = 16√5/√2
so altitude of the equilateral triangle is √3/2 × side
= 16√15/√8
 

Answer 2

let the side of square= xcm
x√2= 12√5
x=12√5/2
4x= perimeter of square= perimeter of triangle
4×12√5/2= perimeter of triangle [substituting x]
2×12×√2×√5= perimeter of triangle
now simplify and find the answer