Question

Katrina buys a 52​-ft roll of fencing to make a rectangular play area for her dogs. Use ​2(ℓ+​w)=52 to write a function for the​ length, given the width. Graph the function. What is a reasonable domain for the​ situation? Explain.

Answer 1

To write a function for the length, given the width, use the equation provided and solve for ℓ. Graph the function and explain a reasonable domain for the situation.

Step-by-step explanation:

To write a function for the length, given the width, we can use the equation provided: 2(ℓ+​w)=52. We will solve for ℓ and graph the function.

1. Start with the equation: 2(ℓ+​w)=52
2. Distribute the 2: 2ℓ + 2w = 52
3. Move the 2w to the other side: 2ℓ = 52 - 2w
4. Divide both sides by 2: ℓ = 26 - w

The equation for the length in terms of the width is: ℓ = 26 - w. To graph this function, we can plot points by assigning values to w and calculating the corresponding values of ℓ. A reasonable domain for this situation would be positive values of width that are less than or equal to 26, since the length cannot be negative and cost constraints limit the width.