A square and a rectangle have equal areas. The length of the rectangle is 9 cm longer than the side of the square and the width of the recangle is 6 cm shorter than the side of the square. How long is the side of the square?
side of square --- x
area of square = x^2
length of rectangle = +9
width of rectangle = x-6
area of rectangle = (x+9)(x-6)
It says the areas are equal
so solve
(x+9)(x-6) = x^2
To solve this problem, we need to use the information given about the relationship between the square and the rectangle.
Let's suppose the side length of the square is "x" cm.
According to the problem, the length of the rectangle is 9 cm longer than the side of the square. So, the length of the rectangle is x + 9 cm.
Also, it is given that the width of the rectangle is 6 cm shorter than the side of the square. Therefore, the width of the rectangle is x - 6 cm.
The area of a square is given by the formula A = side^2, and the area of a rectangle is given by the formula A = length × width.
Given that the areas of the square and rectangle are equal, we can equate the two formulas: x^2 = (x + 9)(x - 6).
Now, let's solve this equation to find the value of x, which represents the length of the side of the square.
Expanding the right side of the equation, we have x^2 = x^2 + 3x – 54.
Rearranging the terms, we get 0 = 3x – 54.
Adding 54 to both sides of the equation, we obtain 54 = 3x.
Dividing both sides of the equation by 3, we find x = 18.
Therefore, the length of the side of the square is 18 cm.
To get this answer, we used the information given about the relationships between the square and the rectangle, and then solved the resulting equation algebraically.