Final answer:
To find the dimensions of the rectangular dog pen with an area of 100 square feet, set up an equation and solve for the width and length. The dimensions of the dog pen are 5 feet by 15 feet.
Step-by-step explanation:
To find the dimensions of the rectangular dog pen, we can set up an equation using the given information. Let's say the width of the dog pen is x feet. Since the length must be 10 feet longer than the width, the length will be x + 10 feet. The area of a rectangle is calculated by multiplying the length by the width. So we have the equation (x + 10)(x) = 100. To solve this equation, we can expand it to x^2 + 10x = 100, and then rearrange it to form a quadratic equation: x^2 + 10x - 100 = 0. We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. The solutions to this equation are x = -20 or x = 5. Since the width cannot be negative, we can discard the solution x = -20, leaving us with the width of the dog pen as x = 5 feet. Therefore, the dimensions of the dog pen are 5 feet by 15 feet.