A 3 foot long pole leans against a wall. The bottom is 5 feet from the wall. How much farther should the bottom be pulled away from the wall so that the top moves the same amount down the wall?
looks like a typo.
A 3 foot long pole cannot be 5 feet away from the wall and touch it.
To solve this problem, we can use the concept of similar triangles.
Let's denote the distance the bottom of the pole needs to be pulled away from the wall as 'x'. When the bottom is pulled away, the top of the pole will move down the wall by the same amount 'x'.
Consider the right triangle formed by the pole, the floor, and the wall. We have a 3-4-5 right triangle, where the base (5 feet) is the distance from the wall to the bottom of the pole, and the height (3 feet) is the length of the pole.
When the bottom of the pole is pulled away by 'x' feet, it creates a similar triangle with the same angles. The new triangle also maintains the same ratios between its sides.
Since the length of the pole (3 feet) corresponds to the height of the triangle, we can set up the following proportion:
(original base + x) / original height = original base / original height
Simplifying the proportion, we get:
(5 + x) / 3 = 5 / 3
To solve for 'x', we can cross-multiply and solve the resulting equation:
5 + x = 15
Subtracting 5 from both sides:
x = 10
Therefore, the bottom of the pole should be pulled away from the wall by 10 feet so that the top moves the same amount down the wall.