Defined Distances
Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?
Age
11 to 14
Challenge level
Problem
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.
Student Solutions
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 $11+2+12=25$.