You may also like

problem icon

Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

problem icon

Ladder and Cube

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?

problem icon

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Weekly Problem 23 - 2007

Stage: 3 and 4 Challenge Level: Challenge Level:1

2

The side of length 5cm cannot be the hypotenuse of the right-angled triangle as it is shorter than the side of length 6cm. If the 6cm side is the hypotenuse, then the third side of the triangle has length $\sqrt{11}$cm. If the 6cm side is not the hypotenuse, then the hypotenuse has length $\sqrt{61}$cm. These are the only two possibilities.

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem