DeeDee draws a rectangle with sides measuring x inches and y inches. She dilates the rectangle using a scale factor of 14. What is the area of the original rectangle in terms of x and y? What is the area of the dilated rectangle? How many times greater is the area of the original rectangle compared to the area of the dilated rectangle? Explain your answers and show all your work.
The area of the original rectangle is given by the formula: A = length * width. In this case, the length is x inches and the width is y inches. So, the area of the original rectangle is xy.
The area of the dilated rectangle is found by multiplying every linear dimension of the original shape by the scale factor, and since the scale factor is 14, the area of the dilated rectangle is (14x) * (14y) = 196xy.
To find how many times greater the area of the original rectangle is compared to the dilated rectangle, we need to divide the area of the original rectangle by the area of the dilated rectangle. So, the ratio is:
Original area / Dilated area = xy / 196xy
= 1 / 196
Therefore, the area of the original rectangle is 196 times greater than the area of the dilated rectangle.