The ladder leans on top of the wall 12ft. If the foot of the ladder is 5ft.from the wall,ron the length of the ladder
this is a Pythagorean triple ... 5-12-13
A ladder base is 4ft in ladders is 12ft how far up wall is it
To find the length of the ladder, we can use the Pythagorean theorem.
The Pythagorean theorem 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 forms the hypotenuse, and the distance from the foot of the ladder to the wall is one of the other two sides. Let's call this distance "a".
The height of the ladder on the wall is the remaining side. Let's call this distance "b".
We are given that the foot of the ladder is 5ft. from the wall, so we have:
a = 5ft.
The ladder leans on top of the wall, which means it forms a right angle with the wall. Therefore, we have a right triangle.
The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
where c represents the length of the ladder.
Substituting the given values into the equation, we have:
c^2 = 5^2 + b^2
c^2 = 25 + b^2
We are also given that the ladder leans on top of the wall 12ft., so the height of the ladder on the wall is 12ft. Therefore, b = 12ft.
Substituting this value into the equation, we have:
c^2 = 25 + 12^2
c^2 = 25 + 144
c^2 = 169
Taking the square root of both sides to solve for c, we have:
c = √(169)
c = 13
Therefore, the length of the ladder is 13ft.
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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, and the wall and the distance from the foot of the ladder to the wall act as the other two sides of the right triangle.
Let's use "x" to represent the length of the ladder:
x^2 = (5ft)^2 + (12ft)^2
Simplifying this equation:
x^2 = 25ft^2 + 144ft^2
x^2 = 169ft^2
Taking the square root of both sides to solve for x:
x = √169ft^2
x = 13ft
So, the length of the ladder is 13ft.