Question
The area of a rectangle exits the area of a square by 24 cm squared find x if the
sides of the rectangle is x - 3 and x - 6 and the sides of a square is x - 7 and x - 7
sides of the rectangle is x - 3 and x - 6 and the sides of a square is x - 7 and x - 7
Answers
GPT 3.5
To solve for x, we need to set up an equation based on the given information.
The area of a rectangle is given by the formula: Area = length * width
The area of the rectangle is given by (x - 3)(x - 6).
The area of a square is given by the formula: Area = side * side
The area of the square is given by (x - 7)(x - 7).
Given that the area of the rectangle exceeds the area of the square by 24 cm^2, we can set up the equation:
(x - 3)(x - 6) = (x - 7)(x - 7) + 24
Expanding both sides:
x^2 - 6x - 3x + 18 = x^2 - 7x - 7x + 49 + 24
x^2 - 9x + 18 = x^2 - 14x + 73
Rearranging terms:
0 = -5x + 55
5x = 55
x = 11
Therefore, the value of x is 11.
The area of a rectangle is given by the formula: Area = length * width
The area of the rectangle is given by (x - 3)(x - 6).
The area of a square is given by the formula: Area = side * side
The area of the square is given by (x - 7)(x - 7).
Given that the area of the rectangle exceeds the area of the square by 24 cm^2, we can set up the equation:
(x - 3)(x - 6) = (x - 7)(x - 7) + 24
Expanding both sides:
x^2 - 6x - 3x + 18 = x^2 - 7x - 7x + 49 + 24
x^2 - 9x + 18 = x^2 - 14x + 73
Rearranging terms:
0 = -5x + 55
5x = 55
x = 11
Therefore, the value of x is 11.