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.

We write system of equations:

O = 5*a
P = 15*a
a,b,c =?

a + b + c = 5a             b + c = 4a
a*b/2 = 15a                 b/2 = 15

Now we calculate b and remaining sides:
b = 30

30 + c = 4a
c^2= 30^2 + a^2
(4a - 30)^2 = 900 + a^2
16a^2 - 240a + 900 = 900 + a^2
15a^2 = 240a
a = 16

that means that c = 4*16-30 = 34