A rectangular fish pond is 21ft(squared) in area. If the owner can surround the pond with a 20 foot fence, what are the dimensions of the pond?
3 by 7 feet
To find the dimensions of the rectangular fish pond, we'll use the given information that the area is 21 square feet and the owner can surround it with a 20-foot fence.
Let's assume the length of the fish pond is L feet and the width is W feet.
The perimeter of the pond is equal to the sum of all sides, which can be represented as:
Perimeter = 2L + 2W
We also know that the owner can surround the pond with a 20-foot fence, so:
Perimeter = 20
Now, we'll substitute the value of the perimeter using the equation and solve for one variable:
2L + 2W = 20
To simplify the equation, we can divide both sides by 2:
L + W = 10
Next, we'll solve for one variable in terms of the other variable.
Let's solve for L:
L = 10 - W
Now, we'll use the area formula to find the dimensions of the pond.
Area = Length × Width
21 = L × W
Substituting the value of L:
21 = (10 - W) × W
Expanding the equation:
21 = 10W - W^2
Rearranging the equation:
W^2 - 10W + 21 = 0
Now, we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use factoring to find the values of W.
Factoring the quadratic equation:
(W - 3)(W - 7) = 0
So, we have two possible solutions: W = 3 or W = 7.
Now, let's substitute these values back into our equation for L:
When W = 3, then L = 10 - 3 = 7
When W = 7, then L = 10 - 7 = 3
Therefore, the dimensions of the rectangular fish pond can be either 7ft by 3ft or 3ft by 7ft.