Question

The lengths of the sides of a triangle are integers,and it's area is also integer. One side is 21and the perimeter is 48. Find the shortest side.

Answer 1

ans:84

Sum of other 2 sides = 27.

=> If one side = x, other = 27 - x.

Using Heron's formula,

=> A^2 = 24*3*(24-x)*(x-3)

RHS must be a perfect square

=> A^2 = 6^2 * 2 * (24-x)(x-3) is a perfect square

=> x = 10, Other side = 17

=> shortest side = 10 cm.

Other sides are 17 and 21 cm,

Area = 84 sq cm.