New photo imaging techniques on computers allow artists to distort an image from its original shape. Figure 1 is a square image (X x X). Figure 2 is stretched 4 units wider and shrunk 4 units shorter than figure 1. (x+4)(X-4).
How many square units greater is the area of Figure 1 than the area of Figure 2?
Please solve and explain. Thanks.
difference = x^2 - (x^2 - 16) = 16
To find the difference in area between Figure 1 and Figure 2, we need to calculate the area of each figure and then subtract the area of Figure 2 from the area of Figure 1.
Let's start by calculating the area of Figure 1, which is a square with sides of length X. The formula for the area of a square is length times width, so the area of Figure 1 is X * X = X^2.
Next, let's calculate the dimensions of Figure 2. We are given that it is stretched 4 units wider and shrunk 4 units shorter than Figure 1. So the length of Figure 2 would be X + 4, and the width of Figure 2 would be X - 4.
Now, we can calculate the area of Figure 2. The area of Figure 2 is (X + 4) * (X - 4).
To find the difference in area, we subtract the area of Figure 2 from the area of Figure 1:
Area difference = Area of Figure 1 - Area of Figure 2
Area difference = X^2 - (X + 4)(X - 4)
To simplify the expression, we can multiply the terms (X + 4)(X - 4):
Area difference = X^2 - (X^2 - 16)
Area difference = X^2 - X^2 + 16
Area difference = 16
Therefore, the area of Figure 1 is 16 square units greater than the area of Figure 2.
To find the area of Figure 1 and Figure 2, we need to know the value of X. However, we are given that Figure 2 is "stretched 4 units wider and shrunk 4 units shorter than figure 1." Let's assume the original width and height of Figure 1 are denoted by W1 and H1.
According to the given information, the dimensions of Figure 2 can be expressed as (W1 + 4) and (H1 - 4). Therefore, the area of Figure 1, A1, can be calculated as:
A1 = W1 * H1
The area of Figure 2, A2, can be calculated as:
A2 = (W1 + 4) * (H1 - 4)
To find the difference in area between Figure 1 and Figure 2, we subtract A2 from A1:
Area Difference = A1 - A2 = (W1 * H1) - ((W1 + 4) * (H1 - 4))
Now, we need a specific value for X to calculate the exact area difference.