Question

Part A: If someone walks along the outside of the garden from point A to point B, what percent of the gardens border would they have walked around? Round your answer to the nearest whole percent.

Part B: In the designers proposal they state that paths EC and DB each measure 100 feet. They also state that the garden will require 140 feet of hedges. Are their numbers reasonable? Explain your reasoning

Answer 1

Part A: The exact percentage of the garden's border that would be walked around depends on the shape and dimensions of the garden. However, it is likely to be close to 100%, unless the garden is highly irregularly shaped.

Part B: The numbers in the designer's proposal are likely to be reasonable. To determine if this is the case, it may be useful to calculate the perimeter of the garden (sum of the lengths of all its sides). If the garden has four sides, the perimeter would be 400 feet (2100 + 2140). The total length of the paths is 200 feet, leaving 200 feet for the hedges which is a reasonable amount. If the garden has more than four sides, the amount of hedging required could be more than 140 feet.

Answer 2

In the graph, we can see that the circle is divided into four pieces, by two axes which is the diameters. When an angle is a central angle, the opposed arc is the same value. Since angle m

So, arc AB = 90º - arc EA ; 90º - 50º= 40º

So, which percentage of the garden's border is AB?

40º/360º = 20/180º = 10/90º = 1/9 = 0.111 x 100% = 11.1% = 11%

So, the person has walked 11% of the whole garden