Question 283044
A 26 ft long ladder rests against a wall. The distance from the base of the wall to the bottom of the ladder is x. The height at which the ladder rests against the wall is x + 14. Find the distance, x, from the base of the wall tithe bottom of the ladder. Please show steps in solving this word problem.

You can imagine that the the ladder , the wall and the floor make a right angle.

The ladder is the hyotenuse

AND the floor and the wall form the legs of the right angled triangle.

26^2= x^2 + ( x+14)^2

676= x^2 +x^2 +28x +196

2x^2+28x-480 =0

2x^2 +40x -12x -480=0

2x(x+40)-12(x+40)=0

(2x-12)(x+40)=0

2x=12 
x=6 feet distance from the base to the bottob of the ladder