A ladder is placed so its foot is 2m from a wall. The ladder touches the top of a 2m fence that is 1.5m from the wall. How high up the wall does the ladder reach?

Draw a diagram. Using similar triangles, see that

h/2 = 2/1.5

Oops

Make that

h/2 = 2/(2-1.5) = 2/0.5

h = 8

To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the ladder forms a right triangle with the wall and the ground. The foot of the ladder is 2m from the wall, so one side of the triangle is 2m. The ladder touches the top of the 2m fence, which is 1.5m from the wall, so the other side of the triangle is 1.5m.

Let's label the height up the wall that the ladder reaches as 'x'. Now we can set up the equation using the Pythagorean theorem:

x^2 = 2^2 - 1.5^2

Simplifying the equation, we have:

x^2 = 4 - 2.25

x^2 = 1.75

To find the value of x, we take the square root of both sides:

x = √1.75

x ≈ 1.32

Therefore, the ladder reaches approximately 1.32m up the wall.