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Answer: The correct option is (C) $342.
Step-by-step explanation: Given that Mr. Williams is building a sand box for his children and is costs $228 for the sand if he builds a rectangular-sand box with dimensions 9 ft by 6 ft.
We are to find the cost of the sand if he decides to increase the size to
Since the box is empty from inside, so we will be considering the perimeter of the box, not area.
The perimeter of the rectangular-sand box with dimensions 9 ft by 6 ft is
and the perimeter of the rectangular-sand box with dimensions is
Now, we will be using the UNITARY method.
Cost of sand for building rectangular-sand box with perimeter 30ft = $228.
So, cost of sand for building rectangular-sand box with perimeter 1 ft will be
Therefore, the cost of sand for building rectangular-sand box with perimeter 45 ft is given by
Thus, the required cost of the sand is $342.
Option (C) is CORRECT.