the larger leg of a right triangle is 7ft longer than its samller leg. the hypotenuse is 1ft longer than the larger leg. how many feet long is the samller leg?

Answer 1

smaller leg ---- x , where x is a positive number
larger leg ------ x+7
hypotenuse ----- x+8

x^2 + (x+7)^2 = (x+8)^2
x^2 + x^2 + 14x + 49 = x^2 + 16x + 64
x^2 - 2x - 15 = 0
(x-5)(x+3) = 0
x = 5 or x is a negative ----> no good

so the 3 sides are:
5 , 12 and 13

check:
is 5^2 + 12^2 = 13^2 , sure is!!!