# Sunday Times Teaser 3176 – Equal Shares

*by Howard Williams*

#### Published Sunday August 06 2023 (link)

When I married, my wife insisted that everything be equally shared between us, which I readily agreed to, provided it included the gardening.

The garden is rectangular, with a smaller rectangular vegetable plot, of different relative dimensions, in one corner, the area of which is less than 7 per cent of that of the whole garden. The rest of the garden is lawned.

To satisfy my wife, I constructed the shortest straight length of partition that would split the garden in half, so that half the vegetable plot and half the lawn were each side of the partition. The length of the partition was 30 metres, which exactly equalled the perimeter of the vegetable plot. Both before and after partitioning, all side lengths were an exact number of metres.

What is the area of the lawn in each half?

A variation of Brian’s program (checking all the requirements).