The Lawn An Investigation

Two men Tom and Dick were going to cut the grass on their square lawn. They agreed that each should cut one-half of the area. Tom went first and cut a border 3 metres wide all the way round as shown in the diagram. After doing a few calculations, Dick agreed that exactly one-half had been cut and happily cut the rest. What was the area of the lawn? Border 3m

Solution:- The Lawn Let x = length of the outside square. Then length of inside square is x-6. So the area of bit cut = Area inside square x 2 - (x-6) 2 = (x-6) 2 Rearranging gives x 2 – 24x +72 = 0 This requires the quadratic formula for its solution. This gives x = and the corresponding area as 419.8m 2

Exercises Exercise 1. Suppose the garden was such that the border cut by Tom had actually been 5 metres wide all the way round, what would the area of the lawn be now? Exercise 2. If the border cut by Tom had been ‘a’ metres all the way round, show that the area of the lawn is given by the expression A = 8a2(3+2√2).