A fence that is 4 metres tall runs parallel to a tall building at a distance
of 1 metre from the building. What is the length of the shortest ladder
that will reach from the ground over the fence to the wall of the building?
We form a rt. triangle:
X = 1 m. = Hor. side.
Y = 4 m. = Ver. side.
Z = Hyp. = Length of the ladder.
Z^2 = X^2 + Y^2
Z^2 = 1^2 + 4^2 = 17
Z = 4.1 m.
To find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled 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 case, the wall of the building, the ground, and the ladder form a right-angled triangle. The height of the fence is one of the sides, and the distance from the fence to the building is the other side.
Let's call the length of the ladder "L", the height of the fence "H", and the distance from the fence to the building "D". According to the Pythagorean theorem, we have:
L² = H² + D²
In this case, H is given as 4 meters and D is given as 1 meter. We can substitute these values into the equation to find the length of the ladder:
L² = 4² + 1²
L² = 16 + 1
L² = 17
To solve for L, we take the square root of both sides:
L = √17
Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately √17 meters.