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

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Puzzles and Curious Problems by Henry Ernest Dudeney: $242$

Correcting a Blunder
Mathematics is an exact science, but first-class mathematicians are apt, like the rest of humanity, to err badly on occasions.
On referring to Peter Barlow's Elementary Investigation of the Theory of Numbers, we hit on this problem:
"To find a triangle such that its three sides, perpendicular, and the line drawn from one of the angles bisecting the base
may all be expressed in rational numbers."
He gives as his answer the triangle $480$, $299$, $209$, which is wrong and entirely unintelligible.
Readers may like to find a correct solution when we say that all the five measurements may be in whole numbers,
and every one of them less than a hundred.
It is apparently intended that the triangle must not itself be right-angled.


Solution

Solution 1

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


Solution 2

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


Dudeney adds:

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


Historical Note

The first solution was the work of Dudeney.

The second solution was the work of Victor Meally.


Sources

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