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 a rectangle is given by the formula A = length * width.
So, the area of the original rectangle is A = x * y.
The dilated rectangle has sides measuring 14 times x and 14 times y. Therefore, the length and width of the dilated rectangle are 14x and 14y, respectively.
The area of the dilated rectangle is A' = (14x) * (14y) = 196xy.
To find how many times greater the area of the original rectangle is compared to the area of the dilated rectangle, we can divide their areas.
(area of original rectangle) / (area of dilated rectangle) = (A) / (A') = (x * y) / (196xy).
We can simplify this expression by canceling out the x and y terms.
(area of original rectangle) / (area of dilated rectangle) = 1 / 196.
Therefore, the area of the original rectangle is 196 times greater than the area of the dilated rectangle. This means the original rectangle is much larger than the dilated rectangle.