Henry Ernest Dudeney/Puzzles and Curious Problems/162 - Find the Triangle/Solution

by : $162$

 * Find the Triangle
 * The sides and height of a triangle are four consecutive whole numbers.
 * What is the area of the triangle?

Solution

 * The sides of the triangle are $13$, $14$, and $15$, making $14$ the base, the height $12$, and the area $84$.


 * There is an infinite number of rational triangles composed of three consecutive numbers, like $3$, $4$ and $5$, and $13$, $14$, and $15$,
 * but there is no other case in which the height will comply with our conditions.