As Long as Possible

Age 11 to 14

ShortChallenge Level Yellow star

$14 \; \text{cm}$ . The length of

$AD$ must be less than

$15 \; \text{cm}$ , since

$15 \; \text{cm}$ would be its length if all four points lay in a straight line. However, by making angles

$ABC$ and

$BCD$ close to

$180^{\circ}$ ,

$AD$ can be made close to

$15 \; \text{cm}$ in length.

As the length of

$AD$ is a whole number of centimetres, its maximum value, therefore is

$14\; \text{cm}$

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

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