A13 foot ladder leans on a wall. the bottom of the ladder is 5 feet from the wall. if the bottom is pulled out 3 feet farther from the wall, how far does the top of the ladder move down the wall? (hint: the ladder, wall and the ground form a right triangle.)

This requires Pythagoras' theorem which says that the square of the hypotenuse = square of another side + the square of another side.
Therefore, a² = b² + c² where a is the length of the ladder, and b and c are the wall and floor.

If the ladder is 13 feet long, and the bottom of the ladder is 5 feet long then:
13² = 5² + c²
So 13² - 5² = c²

So c² = 144, and √144 = 12. So c = 12.

The second part is:
13² = 8²( because 5 + 3 = 8) + c²
Therefore, 13² - 8² = c²
c² = 105
c = √105 so c= 10.25 (rounded to 2 dp)

Finally, since c indicates how high the ladder is against the wall, to find the distance moved you need to do 12 - 10.25 so the distance moved is 1.75 feet.

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!