suppose that the length of one leg of a right triangle is 2 inches less than the length of the other leg.the length of hypotenuse is 10 inches.find the length of each leg.

Answer 1

Just good ol' Pythagoras here ...

x^2 + (x-2)^2 = 10^2
x^2 + x^2 - 4x + 4 - 100 = 0
2x^2 - 4x - 96 = 0
x^2 - 2x - 48 = 0
(x - 8)(x + 6) = 0
x = 8 or x = -6, but we can't have a negative side

so the triangle is 8 by 6 by 10

(which you might recognize as double the well-known 3-4-5 right angled triangle)