A tool shed, 250cm high and 100cm deep, is built agaisnt a wall. Calculate the shortest ladder that can reach from the ground, over the shed, tot he wall behind.

To calculate the shortest ladder that can reach from the ground, over the shed, to the wall behind, you can use the Pythagorean theorem.

Let's assume the ladder forms a right-angled triangle with the ground and the wall. The height of the tool shed is the height of one side of the triangle, the depth of the shed is the other side, and the length of the ladder is the hypotenuse.

Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides, we can calculate the length of the ladder.

The equation is:

ladder length^2 = shed height^2 + shed depth^2

Plugging in the given values:

ladder length^2 = 250cm^2 + 100cm^2

ladder length^2 = 62500cm^2 + 10000cm^2

ladder length^2 = 72500cm^2

To solve for the ladder length, we need to find the square root of both sides:

ladder length = √72500cm^2

Calculating the square root gives us:

ladder length ≈ 269.26cm

Therefore, the shortest ladder that can reach from the ground, over the shed, to the wall behind is approximately 269.26cm.

The shortest length of the ladder is the length of the diagonal of a right triangle with horizontal and vertical sides equal to 100cm and 250cm respectively.

Solve for the diagonal using Pythagoras theorem.