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Problem of the Week
Problem B
Don’t Get Mowed Over!

Jon has a grass cutting business. Three of the lawns that he cuts are shown. The lawns are shaded in green and all angles are right angles. His lawnmower can cut a swath of width \(1\) metre.

A 25 metre by 40 metre rectangle labelled The Ngans’ Lawn. The entire area of the rectangle is shaded green.A figure shaped like a capital L labelled The Jones’ Lawn. The L-shape is formed by a first rectangle that is 40 metres tall and 20 metres wide and a second rectangle that is 20 metres tall and 25 metres wide placed on the right edge of the first rectangle. The entire area of the L-shape is shaded green.A larger rectangle that is 35 metres tall and 50 metres wide with a smaller rectangle that is 10 metres tall and 25 metres wide inside. The area inside the larger rectangle but outside the smaller rectangle is shaded green and is labelled The Bhutus’ Lawn. The distance from the right edge of the smaller rectangle to the right edge of the larger rectangle is 15 metres. The distance from the bottom edge of the smaller rectangle to the bottom edge of the larger rectangle is 10 metres.

  1. Which lawn will take the longest to cut? Explain your reasoning.

  2. His lawnmower travels at \(3\) km per hour. What area of lawn, in \(\text{ m}^2\), can he cut in one hour?

  3. How long, in minutes, will it take him to cut each lawn?

Themes: Geometry & Measurement, Number Sense