Some parks contain fenced gardens. Suppose that it costs $80 to build each metre of fence, including materials and labour.
a) How much does it cost to enclose a square with an area of 120 m²? Express your answer to the nearest dollar.
b) Predict whether the total cost of enclosing two squares with an area of 60 m² each is the same as your answer for part a).
c) Test your prediction from part b) and describe your findings.
part a) The first step is trying to find the square root of 120 by using a calculator. The square root is also the same value as one side of the square garden.
√120 = 10.95
Because there are 4 sides in a square, you need to multiply 10.95 by 4.
10.95 x 4 = 43.8
Then, you need to multiply the number above by $80 to the the final answer.
43.8 x $80 = $3504
The cost of enclosing a square with an area of 120 m² is $3504
part b) Following the same procedure we used for part a), find the square root of one square with an area of 60 m²
√60 = 7.74
7.74 x 4 = 30.96
30.96 x 80 = 2476.8
And because we are finding the area of two 60 m² fenced gardens, multiply that previous answer by two.
2476.8 x 2 = $4953.6
As you can see, the results are Not The Same.
c) I predicted that the costs for the fenced gardens would not be the same because two 60 m² squares have a total of 8 sides, and a 120 m² only has four sides, therefore I knew that the area would of the 60 m² would be larger because of the greater amount of sides.