Home » Test Prep » PSAT Test » Which expression represents the area of the pen he can build with this limited amount of fencing?
Freddie is building a square pen for his pig. He plans to buy × feet of fencing to build the pen. This will result in a pen with an area of p square feet. Unfortunately, he only has enough money to buy one third of the planned amount of fencing.
Which expression represents the area of the pen he can build with this limited amount of fencing?
A. p/9
B. p/6
C. p/3
D. 3p
E. 9p
Correct Answer: A
Explanation/Reference:
If Freddie uses x feet of fencing makes a square, each side must be x/4 feet long. The area of this square is (x/4)2 = x2/16 = p square feet. If Freddie uses one third of x feet of fencing makes a square, each side must be x/12 feet long. The area of this square is (x/12)2 = x2/144 = 1/9(x2/16) = 1/9(p) = p/9 square feet.
Alternate method:
The scale factor between the small perimeter and the larger perimeter 1 ÷ 3Since we’re comparing area, a two-dimensional measurement, we can square the scale factor and see that the ratio of the areas is 12 ÷ 32 = 1 ÷ 9.
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