a ladder is placed 5ft away from a house. the ladder comes up to 12ft on the side of the house. how long is the ladder?

Pythagorean Theorem to the rescue!!

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2

13 = c

a 13ft ladder is placed 12ft on the side of a house. how far is the base of the ladder to the house?

Well, it seems like the ladder is quite the overachiever! It's not only reaching the side of the house, but it's also reaching for the stars! In this case, the length of the ladder can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides. So, if we use the ladder as the hypotenuse, the distance from the house as one of the sides, and the height of the ladder as the other side, we can find the answer. By plugging in the values, we get:

(c^2) = (a^2) + (b^2)
(c^2) = (5^2) + (12^2)
(c^2) = 25 + 144
(c^2) = 169

Now, if we take the square root of both sides, we find that the length of the ladder is equal to 13ft. So, it turns out that the ladder has made its way into being a "lucky" 13!

To find the length of the ladder, 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 is the hypotenuse, and the distance from the ladder to the house is one of the other two sides. Let's call the distance from the ladder to the house 'a' and the length of the ladder 'c'.

According to the problem, a = 5 ft, and the ladder goes up to 12 ft on the side of the house.

Using the Pythagorean theorem, we can calculate c:

c^2 = a^2 + b^2

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

Taking the square root of both sides, we get:

c = √169

c = 13

Therefore, the length of the ladder is 13 ft.

To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this scenario, the ladder acts as the hypotenuse, and the distance from the base of the ladder to the house acts as one side of the right triangle. The height of the ladder on the side of the house is the other side of the right triangle.

So, given that the ladder comes up to 12ft on the side of the house and is placed 5ft away from the house, we can set up the equation as follows:

Ladder length^2 = distance from the base of the ladder to the house^2 + height of the ladder on the side of the house^2

Ladder length^2 = 5ft^2 + 12ft^2

Ladder length^2 = 25ft^2 + 144ft^2

Ladder length^2 = 169ft^2

Taking the square root of both sides, we get:

Ladder length = √169ft^2

Ladder length = 13ft

Therefore, the ladder is 13ft long.