Question

The foot of an extension ladder is 10 ft from a wall. the ladder is 2 ft longer than the height that it reaches on the wall. how far up the wall does the ladder reach

Answer 1

this makes a right triangle with hypotenuse x+2 and legs 10 and x

10²+x²=(x+2)²

100 + x² = x²+4x+4

100=4x+4

4x=96

x=24, the height we are looking for

Answer 2

base: 10

height: x

diagonal: x + 2

base² + side² = diagonal²

(10)² + (x)² = (x + 2)²

100 + x² = x² + 4x + 4

100 = 4x + 4

96 = 4x

24 = x

Answer: 24 ft