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Problem of the Week
Problem C
All Equal

Using two cuts, we want to divide the \(6\) m by \(6\) m grid shown into three regions of equal area.

A square is divided into a 6 by 6 grid of identical squares. The bottom left vertex of the square is labelled P, the top left vertex is R, the top right vertex is Q, and the bottom right vertex is M. The five points on top side RQ where the vertical grid lines meet RQ are labelled S, T, U, V, and W, from left to right. The five points on right side QM where the horizontal grid lines meet QM are labelled G, H, J, K, and L, from top to bottom.

One way to do so is by making a horizontal cut through \(H\) and a second horizontal cut through \(K\). This method of cutting the grid works, but is not very creative.

To make things a little more interesting, we must still make two straight cuts, but each cut must start at point \(P\). Each of these two cuts will pass through a point on the outer perimeter of the grid.

Find the length of each cut. Round your answer to one decimal.

Themes: Geometry & Measurement, Number Sense