SOLUTION: Show that if the length of one leg of a right triangle and the hypotenuse are consecutive integers, then the square of the length of the second leg is equal to the sum of the lengt

Algebra ->  Triangles -> SOLUTION: Show that if the length of one leg of a right triangle and the hypotenuse are consecutive integers, then the square of the length of the second leg is equal to the sum of the lengt      Log On


   

Question 775198: Show that if the length of one leg of a right triangle and the hypotenuse are consecutive integers, then the square of the length of the second leg is equal to the sum of the lengths of the first leg and the hypotenuse.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
L= length of one leg
L%2B1= length of hypotenuse
x= length of the other leg
According to Pythagoras;
x%5E2%2BL%5E2=%28L%2B1%29%5E2
x%5E2%2BL%5E2=L%5E2%2B2L%2B1
x%5E2%2Bcross%28L%5E2%29=cross%28L%5E2%29%2B2L%2B1
x%5E2=2L%2B1
x%5E2=L%2BL%2B1
x%5E2=L%2B%28L%2B1%29