Given
It is given that the longer leg is 4 cm longer than the shorter leg.
It is also given that the hypotenuse is 8 cm longer than the shorter leg.
Step-by-step explanation
Let the shorter leg be x.
The longer leg be y.
Then the relation formed is

It is also given that the hypotenuse is 8 cm longer than the shorter leg.
Let the hypotenuse is z.

Then the perimeter of the right triangle is the sum of all the sides.

But to find the value of x , use the Pythagoras theorem.

Substitute the values.

Solve the quadratic equation to find the value of x.

As x cannot be negative , then the value of x is 12.
The length of shorter leg is 12.
The length of longer leg is 12+4=16.
The hypotenuse is 12+8=20.
Now , the perimeter of right triangle is

Answer
The perimeter of the triangle is 48 cm.