Question

The perimeter of a right angled triangle is 5 times the length of the shortest side. The numerical value of the area of the triangle is 15 times the numerical value of the length of the shortest side. Find the lengths of all the three sides of the triangle.

Answer 1

you have 3 unknowns, so you need 3 equations.
perimeter of a right angled triangle is 5 times the length of the shortest side

let a= shortest side, b the other leg, c the hypotenuse
then
a+b+c= 5a , or b+c= 4a
area of the triangle is 15 times the numerical value of the length of the shortest side.

1/2 a b= 15 a, or b=30

a^2+b^2= c^2