for this one how do i set it up?
IF THE SIDE OF A SQUARE ARE DECREASED BY 3CM, THE AREA IS DECREASED BY 81CM^2. WHAT WERE THE DIMENSIONS OF THE ORIGINAL SQUARE?
To solve this problem, let's break it down step by step:
Step 1: Assign variables:
Let's assume that the original side length of the square is represented by "x" centimeters.
Step 2: Determine the area of the original square:
The formula to calculate the area of a square is A = side * side. Therefore, the area of the original square is A = x * x = x^2.
Step 3: Decrease the side length and find the new area:
According to the problem, the side length of the square is decreased by 3 cm. Therefore, the new side length would be (x - 3) cm. Using the formula, the new area can be calculated as (x - 3) * (x - 3) = (x - 3)^2.
Step 4: Set up the equation:
The problem states that when the side length is decreased by 3 cm, the area is decreased by 81 cm^2. This can be written as:
x^2 - (x - 3)^2 = 81.
Step 5: Solve the equation:
Expanding the equation and rearranging the terms, we get:
x^2 - (x^2 - 6x + 9) = 81,
x^2 - x^2 + 6x - 9 = 81,
6x - 9 = 81.
Next, add 9 to both sides of the equation:
6x = 90.
Finally, divide both sides of the equation by 6:
x = 15.
Step 6: Find the dimensions of the original square:
Since the side length is x, the dimensions of the original square are 15 cm by 15 cm.
Therefore, the original square had dimensions of 15 cm by 15 cm.