Answer :
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.
Explanation
Let the shorter leg be x.
The longer leg be y.
Then the relation formed is
[tex]y=x+4[/tex]It is also given that the hypotenuse is 8 cm longer than the shorter leg.
Let the hypotenuse is z.
[tex]z=8+x[/tex]Then the perimeter of the right triangle is the sum of all the sides.
[tex]x+y+z[/tex]But to find the value of x , use the Pythagoras theorem.
[tex]z^2=y^2+x^2[/tex]Substitute the values.
[tex]\begin{gathered} (8+x)^2=(4+x)^2+x^2 \\ 64+x^2+16x=16+x^2+8x+x^2 \\ 64+16x=16+8x+x^2 \\ 64-16+16x-8x-x^2=0 \\ -x^2+8x+48=0 \end{gathered}[/tex]Solve the quadratic equation to find the value of x.
[tex]\begin{gathered} (x-12)(x+4)=0 \\ x=12,-4 \end{gathered}[/tex]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
[tex]\begin{gathered} P=12+16+20 \\ P=48cm \end{gathered}[/tex]Answer
The perimeter of the triangle is 48 cm.