Each side of a square is lengthened by 2 inches. The area of this new, larger square is 81 square inches. Find the length of a side of the original square.
√81 = 9
9 - 2 = 7
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent whole numbers. 2 - 36
X
Well, well, well, we have a square that decided to go on a growth spurt! Let's call the side length of the original square 'x'. So, the new square has a side length of 'x + 2', right? Now, according to your problem, the area of the new square is 81 square inches. So, what's the equation we can cook up here? Well, Area = Side length squared. So, the area of the new square is (x + 2) squared, which gives us 81. Now, let's simplify things. Expand that (x + 2) squared term and set it equal to 81. Solve that equation, and voila! You'll find the length of a side of the original square. Good luck, my square-loving friend!
Let's assume that the length of each side of the original square is 'x' inches.
If each side of the square is lengthened by 2 inches, the new length of each side would be 'x + 2' inches.
The area of a square is given by the formula: Area = side^2.
Thus, the area of the larger square is (x + 2)^2 = 81 square inches.
Expanding this equation gives us x^2 + 4x + 4 = 81.
Subtracting 81 from both sides, we get x^2 + 4x - 77 = 0.
Now, we can solve this quadratic equation to find the value of 'x'.
To solve this problem, we can use algebra. Let's denote the length of a side of the original square as "x".
According to the given information, each side of the original square is lengthened by 2 inches. Therefore, the length of a side of the larger square, which is formed by lengthening each side of the original square, will be "x + 2".
The area of a square is calculated by squaring the length of one of its sides. So, the area of the larger square is (x + 2) * (x + 2), which is equal to 81 square inches.
To find the length of the side of the original square, we need to solve the equation (x + 2) * (x + 2) = 81 for "x".
Expanding the equation, we get x^2 + 4x + 4 = 81.
Rearranging, we have x^2 + 4x - 77 = 0.
Now we can solve this quadratic equation. There are multiple methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.
Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0.
For our equation x^2 + 4x - 77 = 0, a = 1, b = 4, and c = -77.
Plugging these values into the quadratic formula, we get x = (-4 ± √(4^2 - 4*1*(-77))) / (2*1).
Simplifying further, x = (-4 ± √(16 + 308)) / 2.
Calculating, x = (-4 ± √324) / 2.
Since we are looking for the length of a side, which cannot be negative, we can disregard the negative solution.
Therefore, x = (-4 + √324) / 2.
Simplifying, x = (-4 + 18) / 2.
Finally, x = 14 / 2.
Thus, the length of a side of the original square is 7 inches.