Final answer:
To find the side lengths x and y of the adjoining squares, two equations were used based on the total perimeter 150 feet and the area 1125 square feet. The solution is x = 25 feet and y = 5 feet, So the correct answer is c.
Step-by-step explanation:
The problem involves finding the lengths of the sides of two adjoining squares that have a total area of 1125 square feet and can be enclosed with 150 feet of fencing.
The larger square has sides of length x and the smaller square has sides of length y. To solve this, we use the given area and the perimeter.
Firstly, let's calculate the combined perimeter of the two squares. We know that the farmer has 150 feet of fence, so:
P = 2x + 3y = 150
Because one side of the small square uses the same fencing as one side of the large square, we have only three sides of the small square contributing to the perimeter, hence the '3y' term.
Now, let's use the given area to create another equation:
A = x^2 + y^2 = 1125
We have two equations with two unknowns:
P = 2x + 3y = 150
A = x^2 + y^2 = 1125
Solving this system of equations, we find that the solution that fits within the limits of our fencing and area constraints is: x = 25 feet, y = 5 feet
So the correct answer is c) x = 25 feet, y = 5 feet.