Problem

At POTW Doggy Care, there is a need for a new outdoor dog run space. The layout of the dog run space is represented by \(PQRSTU\) in the diagram below.

A grey square is labelled Doggy Daycare. The top left vertex of the square is \(U\), point \(P\) is on its left side, and point \(T\) is on its top side. \(PQRSTU\) is a green six-sided polygon labelled Dog Run Space that wraps around the top left corner of the grey square. To trace the perimeter of the green space, start at \(U\), move down to \(P\), move left to \(Q\), move up past the square to \(R\), move right to \(S\) that is directly above \(T\), move down to \(T\), then move left to \(U\).

The lengths of the two longer sides, \(QR\) and \(RS\), are to be the same, and the lengths of the two shorter sides, \(PQ\) and \(ST\), are to be the same. There will be right angles at each corner.

The dog run space is to be built using a fence along \(PQ\), \(QR\), \(RS\), and \(ST\), and using the walls of the daycare along \(PU\) and \(TU\). The total fencing to be used is \(30\text{ m}\). Determine the dimensions of the dog run space that will give the maximum area for the dog run.

Problem of the Week Problem E Run Dog Run

Problem of the Week
Problem E
Run Dog Run