Answer:
Let x be the length of one side of the first carpet in feet. Then, the area of the first carpet is x^2 square feet.
Let y be the length of one side of the second carpet in feet. Then, the area of the second carpet is y^2 square feet.
From the problem, we know that the sum of the areas of the two carpets is 720 square feet:
x^2 + y^2 = 720
We also know that the difference of the areas of the two carpets is 432 square feet:
x^2 - y^2 = 432
We can solve this system of equations by using the method of substitution. Solving for x^2 in the second equation, we get:
x^2 = y^2 + 432
Substituting this expression for x^2 into the first equation, we get:
y^2 + 432 + y^2 = 720
Simplifying and solving for y, we get:
2y^2 = 288
y^2 = 144
y = 12
Substituting this value of y into the equation x^2 + y^2 = 720 and solving for x, we get:
x^2 + 144 = 720
x^2 = 576
x = 24
Therefore, the dimensions of the first carpet are 24 feet by 24 feet, and the dimensions of the second carpet are 12 feet by 12 feet.
Explanation: