Bairleys rectangular dog pen for his irish setter must have an area of 400 square feet. Also the length must be 50 feet longer than the width. Find the dimentions of the pen
To find the dimensions of the dog pen, we'll set up an equation using the given information.
Let's assume the width of the rectangular dog pen is "x" feet. According to the given condition, the length of the pen will be 50 feet longer than the width, so the length would be "x + 50" feet.
The area of a rectangle is calculated by multiplying its length and width. In this case, we know that the area of the dog pen is 400 square feet. Therefore, the equation becomes:
x * (x + 50) = 400
Now, let's solve this equation step by step to find the dimensions of the pen:
Expanding the equation:
x^2 + 50x = 400
Rearranging terms:
x^2 + 50x - 400 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Factoring is the simplest method in this case:
(x + 20)(x - 20) = 0
Setting each factor equal to zero:
x + 20 = 0 or x - 20 = 0
Solving for x:
x = -20 or x = 20
Since the width cannot be negative (we are talking about a physical pen here), we discard the negative solution. So, the width of the pen is 20 feet.
Now, using the width we found, we can calculate the length:
Length = Width + 50
Length = 20 + 50
Length = 70 feet
Therefore, the dimensions of the dog pen should be 20 feet (width) by 70 feet (length).