Answer:
Explanation:
Let's assume that the length of each side of the smaller square is x inches.
According to the problem, the length of each side of the larger square is 3 inches more than the length of each side of the smaller square. Therefore, the length of each side of the larger square is (x + 3) inches.
The area of a square is calculated by squaring the length of one side. So, the area of the smaller square is x^2 square inches, and the area of the larger square is (x + 3)^2 square inches.
The problem states that the sum of the areas of the squares is 185 square inches. So, we can set up the equation:
x^2 + (x + 3)^2 = 185
Expanding the equation:
x^2 + (x^2 + 6x + 9) = 185
Combining like terms:
2x^2 + 6x + 9 = 185
Rearranging the equation:
2x^2 + 6x - 176 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = 6, and c = -176.
Substituting these values into the formula:
x = (-6 ± √(6^2 - 4 * 2 * -176)) / (2 * 2)
Simplifying:
x = (-6 ± √(36 + 1408)) / 4
x = (-6 ± √1444) / 4
x = (-6 ± 38) / 4
Now we have two possible values for x:
x1 = (-6 + 38) / 4 = 32 / 4 = 8
x2 = (-6 - 38) / 4 = -44 / 4 = -11
Since side lengths cannot be negative, we discard the negative value.
Therefore, the length of each side of the smaller square is 8 inches.
To find the length of each side of the larger square, we add 3 inches:
Length of each side of the larger square = 8 + 3 = 11 inches.
So, the lengths of the sides of the two squares are 8 inches and 11 inches, respectively.