Walk the Plank
A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?
Age
14 to 16
Challenge level
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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.
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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 $x$ = $10\sqrt{2} - 1$.