# Defined Distances

Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

Mark marked out the points $J$, $K$, $L$ and $M$ on a straight line, so that

$JK=13$cm

$KL=11$cm

$LM=14$cm

$MJ=12$cm

What is the distance, in cm, between the two points furthest apart?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

We plot $J$ and $K$ $13$ apart. There are a number of options for where to add $L$ and $M$, but working systematically we find that only one option is consistent with $MJ$ being $12$. The final layout looks like

Image

The distance between the points furthest apart is $11+2+12=25$.