Let c=hypotenuse, a=longer leg, b=other leg
Since the hypotenuse exceeds the longer leg by 2, it is 2 units more than the longer leg. In other words:
Since the perimeter is 40, we can find the other leg by the perimeter formula
where P is the perimeter and a,b,c, are the sides of the triangle
Substitute a+2 into c
Since the missing side (b) can be found by Pytagoreans Thereom, we can say
Solve for b
Substitute a+2 into c
Now plug in in for b to complete the equation
Square both sides
Get all terms to one side
Now plug your quadratic into the quadratic formula to find a (sorry the solver wouldn't format):
if we use a calculator, we get:
or
Now lets find c
Let a=24
Since 24+26=50 which is over 40, 24 is not our answer
Let a=24
Now find b
So the sides are:
a=15,b=8,c=17
Check:
Use the perimeter formula to check
Plug in a=15,b=8,c=17
works