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Answer: 90 cm
Label the blocks
and say the height of the table is $h$
$84+l=h+w$ 
$96+w=h+l$
$l$ and $w$ are on different sides of the equations so add to make them cancel: $$\begin{align}&\qquad 84+l=h+w\ \ \\
&\underline{+\quad 96+w=h+l\ \ }\\
&180 + l+w=2h+l+w\end{align}$$ so $2h=180$ and $h=90$
Table Height
Age 14 to 16
ShortChallenge Level 
Answer: 90 cm
Label the blocks
and say the height of the table is $h$ $84+l=h+w$ $96+w=h+l$$l$ and $w$ are on different sides of the equations so add to make them cancel: $$\begin{align}&\qquad 84+l=h+w\ \ \\
&\underline{+\quad 96+w=h+l\ \ }\\
&180 + l+w=2h+l+w\end{align}$$ so $2h=180$ and $h=90$
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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