Question

The foot of an extension ladder is 9ft from a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive integers. How long is the ladder?

Answer 1

The simplest ratio of sides of a right-angled triangle is the 3:4:5 ratio
so we have 9:x:y, clearly x = 12, and y = 15

check: 9^2 + 12^2 = 15^2 , YES

Answer 2

9^2+x^2=(x+1)^2
81+x^2 = x^2+2x+1
x=40
So, the ladder is 41 ft long.
That's some ladder!