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

by : $242$

 * Correcting a Blunder

Solution

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

Proof
We have:
 * $20^2 + 15^2 = 25^2$, demonstrating that the triangle on the left is right-angled


 * $15^2 + 8^2 = 17^2$, demonstrating that the triangle in the middle is right-angled


 * $15^2 + \paren {28 + 8}^2 = 39^2$, demonstrating that the triangle formed from the two on the right is right-angled


 * The side whose length is $17$ is seen to bisect the base.


 * The area of the whole triangle is $\dfrac 1 2 \times 15 \times 56 = 420$.

adds:
 * Perhaps our readers would like to try their hand at constructing the general solution to triangles of this class.