You may also like

problem icon

Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

problem icon

Rationals Between

What fractions can you find between the square roots of 56 and 58?

problem icon

Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Max Box

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Three rods of lengths $p$, $q$ and $r$ with $p< q< r$ are arranged to form three sides $AB$, $BC$ and $CD$ of an enclosure $ABCD$ with right angles at $B$ and $C$. The diagram shows one possibility but the rods can be exchanged to make different enclosures. The enclosure is completed by joining $A$ and $D$. How should the rods be arranged to make the area of the enclosure as big as possible?