The difference of the area of two squares is 223 square feet and the difference of their perimeters is 24 feet. Find a side of each square.
side of large square = x
side of smaller square = y
x^2 - y^2 = 223
4x - 4y = 24 ---> x - y = 6 ----> x = y+6
sub the last equation into the first and solve
this is simple all u do is put a 4 under all the numbers than you will be left with x-4=y so than you just say x-4=24 an that's your answer :) you can always think me lata
kisses,
To solve this problem, we'll need to set up a system of equations based on the given information.
First, let's define the sides of the two squares. Let the side of the larger square be x and the side of the smaller square be y.
We know that the difference of the area of the two squares is 223 square feet. The area of a square is equal to the side length squared. So we can set up the following equation:
x^2 - y^2 = 223 (Equation 1)
We also know that the difference of their perimeters is 24 feet. The perimeter of a square is equal to 4 times the side length. So we can set up another equation:
4x - 4y = 24 (Equation 2)
Now we have a system of two linear equations (Equation 1 and Equation 2). We can solve this system to find the values of x and y.
Let's solve Equation 2 for x:
4x - 4y = 24
4x = 4y + 24
x = y + 6 (Equation 3)
Now substitute Equation 3 into Equation 1:
(y + 6)^2 - y^2 = 223
y^2 + 12y + 36 - y^2 = 223
12y + 36 = 223
12y = 223 - 36
12y = 187
y = 187/12
Therefore, the side length of the smaller square, y, is approximately 15.58 feet.
Now substitute the value of y into Equation 3 to find x:
x = y + 6
x = 15.58 + 6
x = 21.58
Therefore, the side length of the larger square, x, is approximately 21.58 feet.
So, the side length of the smaller square is approximately 15.58 feet, and the side length of the larger square is approximately 21.58 feet.