Henry Ernest Dudeney/Puzzles and Curious Problems/242 - Correcting a Blunder/Solution 2

by : $242$

 * Correcting a Blunder

Solution

 * Dudeney-Puzzles-and-Curious-Problems-242-solution-2.png

Proof
The triangle in solution is the obtuse triangle whose sides are $66$, $41$ and $85$.

We have:
 * $40^2 + \paren {66 + 9}^2 = 85^2$, demonstrating that the extended triangle is right-angled


 * $9^2 + 40^2 = 41^2$, demonstrating that the triangle on the far right is right-angled


 * $40^2 + \paren {\dfrac {66} 2 + 9}^2 = 58^2$, demonstrating that the triangle formed from the two on the right is right-angled


 * The side whose length is $58$ is seen to bisect the base.


 * The area of the triangle in solution is $\dfrac 1 2 \times 40 \times 66 = 1320$.