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

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $242$. -- Correcting a Blunder
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $280$. Correcting a Blunder