Question

Two window washers, Reba and Nate, lean a ladder against the side of a building so that Reba can wash a window while Nate holds the ladder. The top of the ladder reaches the window, which is 4 meters off the ground. The base of the ladder is 3 meters away from the building. How long is the ladder?

Options:

A) 5 meters

B) 7 meters

C) 8 meters

D) 9 meters

Answer 1

Using the Pythagorean theorem, we calculate the length of the ladder to be 5 meters, which corresponds to answer option A.

Step-by-step explanation:

The question asks for the length of a ladder leaning against a wall, with one end 3 meters away from the building and the other end reaching a window 4 meters above the ground. This is a classic example of a problem that can be solved using the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ladder serves as the hypotenuse of the triangle, the distance from the building to the base of the ladder is one leg, and the height of the window off the ground is the other leg.

To find the length of the ladder, we use the Pythagorean theorem formula: a2 + b2 = c2. Substituting the given values into the formula, we get 32 + 42 = c2, which simplifies to 9 + 16 = c2. Thus, c2 = 25, and by taking the square root of both sides, we find that c (the length of the ladder) is 5 meters.

Therefore, the correct answer is A) 5 meters.