Walk the Plank
A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?
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![Walk the Plank Walk the Plank](/sites/default/files/styles/large/public/thumbnails/content-id-4885-2003-24.gif?itok=DRkHIWaI)
The diagram shows a 1 by x rectangular plank
which fits neatly inside a 10 by 10 square frame.
What is the value of x?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Image
![Walk the Plank Walk the Plank](/sites/default/files/styles/large/public/thumbnails/content-id-4885-2003-24ans.gif?itok=qNuO3vbE)
The figure on the right shows the top left-hand corner of the complete diagram. Note the symmetry which leads to the three measurements of $\frac{1}{2}$. Thus the diagonal of the square can be divided into three portions of lengths:
$\frac{1}{2}$, $x$ and $ \frac{1}{2}$ respectively.
The length of the diagonal $= \sqrt{10^2 + 10^2} = \sqrt{200} = 10 \sqrt{2}$.
So $x$ = $10\sqrt{2} - 1$.