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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.



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
0 0 0
Let the side of square= xcm
x√2= 12√5
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
1 5 1
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