Peter buys 84 yards of fence to make a play area for his puppy. He wants the area to be 28 yards long. What is the area of the play area if he uses the entire fence he bought?
P = 2L + 2W
84 = 2(28) + 2W
84 - 56 = 2W
28 = 2W
14 = W
28 * 2 = 56
84 - 56 = 28
28/2 = 14
so we have 28*14 if rectangle
28* 14 = 392 yd^2
To find the area of the play area, we need to multiply the length and width of the area. In this case, the length is given as 28 yards.
However, we don't have the width of the play area. To find the width, we can use the fact that Peter bought 84 yards of fence to enclose the play area.
Since the play area is enclosed, we can use the perimeter formula to find the width. The perimeter formula for a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, we have P = 84 and L = 28. Plugging in these values into the formula, we get:
84 = 2(28) + 2W
Simplifying the equation, we have:
84 = 56 + 2W
Subtracting 56 from both sides, we get:
28 = 2W
Dividing both sides by 2, we find:
W = 14
So, the width of the play area is 14 yards.
Now that we have both the length and width, we can find the area by multiplying the length and width:
Area = Length × Width
= 28 yards × 14 yards
= 392 square yards
Therefore, the area of the play area is 392 square yards if Peter uses the entire fence he bought (84 yards).