A certain right angled triangle has its area numerically equal to its perimeter. The length of its each side is an even integer. What is the perimeter?

Since the triangle is given to be a right angled triangle, hence we have the sides of the triangle in the ratio 3:4:5.
Now, it is given that the lengths of the sides of the triangle are even integers.
Hence we may assume the sides to be 6, 8 and 10.
(You may also attempt to solve for the sides using the given condition that area = perimeter i.e. ½ b. p = b + p + √b² + p²
i.e. ½ .3x . 4x = 3x + 4x + √3x² +4x²
solving this we get, x = 2)
Now, the sides are 6, 8 and 10.
So, perimeter = 6 + 8+ 10 = 24.
Area = ½ .6.8 = 24.
Hence. the required perimeter is 24.