Question

A square and an equilateral triangle have equal perimeters. If a diagonal of the the square is 24√2 ,then find the area of the triangle

Answer 1

if diagonal is 24√2 then side is 24 so perimeter of the square is 4(24).side of triangle is a. then 3a=96 so a=32 hence area of equilateral triangle is √3a^2/4 =256√3 is the answer

Answer 2

let the side of square be a
sqrt{2}a = 24\sqrt{2 }
a = 24
therefore the perimeter of triangle is 24×4
=96
by the condition,
96= 3×a[let the side of the triangle be a]
or,a=32
so the area of triangle is,
\sqrt {3}/4×32
=8\sqrt{3}