Answer:First, draw a picture.
Distance on ground = 10 feet
Length of ladder (hypotenuse) = x [unknown for now]
Height on wall = x-2
The Pythagorean theorem says, for a right triangle: a2+b2=c2
[note: the hypotenuse, c, is always the longest side]
102 + (x-2)2 = x2
100 + x2 -4x + 4 = x2 [expand using F-O-I-L]
100 -4x + 4 = 0 [subtract x2 from both sides]
104 - 4x = 0 [collect terms]
-4x = -104 [subtract 104 from both sides]
x = 26 [divide both sides by (-4)]
Check:
Is 102 + 242 = 262 ?
100 + 576 = 676 ?
676 = 676 ?yes
Explanation: