Question

"Shirley has two different garden plots, and she wants to fence in each garden plot with the same number of small rocks. Write and solve an equation to find the value of ‘r’ so that the garden plots have the same perimeter."

Answer 1

To find the value of 'r' so that the garden plots have the same perimeter, use the equation Length1 + Width1 = Length2 + Width2. Substitute the given measurements and solve for 'r'.

Step-by-step explanation:

To find the value of 'r' so that the garden plots have the same perimeter, we can use the formula for the perimeter of a rectangle, which is P = 2*(Length + Width). Since each garden plot is a rectangle, the equation for their perimeters would be P1 = 2*(Length1 + Width1) and P2 = 2*(Length2 + Width2). Since the perimeters are the same, we can set them equal to each other: 2*(Length1 + Width1) = 2*(Length2 + Width2). Simplifying this equation, we get Length1 + Width1 = Length2 + Width2. Since the length and width of each garden plot is different, we can substitute them with variables, let's say L1, W1, L2, and W2. So the equation becomes L1 + W1 = L2 + W2.

Now, you didn't mention what values for Length1, Width1, Length2 and Width2 were given, so I'll assume you have the measurements for each garden plot. Let's say Length1 = 10 m, Width1 = 8 m, Length2 = 12 m, Width2 = 6 m. Substituting these values into the equation: 10 + 8 = 12 + 6. Simplifying: 18 = 18. This is a true statement, so the equation is correct. Therefore, the value of 'r' for the garden plots to have the same perimeter is 18.