Being resilient

If you know the perimeter of a right angled triangle, what can you say about the area?

Can you explain what is going on in these puzzling number tricks?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Can you create a Latin Square from multiples of a six digit number?

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?