SOLUTION: The hypotenuse of a right triangle is 4 cm. longer than one leg and 8 cm. longer than the other leg. Solve for the sides using the Pythagorean theorem.

Let x be the longest leg.

Then the shortest leg is (x-4) and the hypotenuse is (x+4).


Write the Pythagoras equation

    (x-4)^2 + x^2 = (x+4)^2

    (x^2 - 8x + 16) + x^2 = x^2 + 8x + 16

     2x^2 = 16x 

     x*(x-8) = 0.


The roots are x= 0 and/or x= 8.  Obviously, only positive root x= 8 is the solution to the problem.


ANSWER.  The legs are 4 cm and 8 cm; the hypotenuse is 12 cm.


Alternatively, the problem can be solved mentally, by noticing that this right-angled triangle
is a standard (3,4,5) Pythagorean triangle.