Question

Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?(1 point)

Responses

108 ft.
108 ft.

10.4 ft.
10.4 ft.

13.4 ft.
13.4 ft.

180 ft.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, the distance from the base of the ladder to the house acts as one of the other sides, and the height of the ladder (what we are trying to find) acts as the other side.

Using the Pythagorean theorem, we have:

(6 ft)^2 + (x ft)^2 = (12 ft)^2

36 + x^2 = 144

x^2 = 144 - 36

x^2 = 108

x ≈ 10.4 ft

Therefore, the ladder will reach a height of approximately 10.4 ft.