Sunday Times Teaser 2651 – Parsnip Farm

by Rex Lanham

Parsnip Farm has a triangular field with one boundary running due north. To divide this field into two smaller triangular fields, a fence is constructed running due east from the southermost point on this boundary.

As a result the northern field is forty percent of the area of the southern field. The lengths of all sides of all fields are whole numbers in furlongs [*] and the southern field has one side that is 25 furlongs long.

What are the lengths of its other two sides?

[*] the furlong is a unit of length – see https://en.wikipedia.org/wiki/FFF_system