DeeDee draws a rectangle with sides measuring 13 inches and 28 inches. She dilates the rectangle using a scale factor of
1
4
. What is the area of the original rectangle? What is the area of the dilated rectangle? How many times greater is the area of the original rectangle to the are of the dilated rectangle? Explain your answers and show your work.(3 points)
The area of a rectangle is given by the formula length * width.
For the original rectangle with sides measuring 13 inches and 28 inches, the area is:
Area = 13 inches * 28 inches
Area = 364 square inches
Now let's calculate the area of the dilated rectangle using a scale factor of 1/4.
To find the new length and width of the dilated rectangle, we multiply the original dimensions by the scale factor:
Length of dilated rectangle = 13 inches * 1/4 = 13/4 inches
Width of dilated rectangle = 28 inches * 1/4 = 28/4 inches = 7 inches
Now we can calculate the area of the dilated rectangle:
Area of dilated rectangle = (13/4 inches) * (7 inches)
Area of dilated rectangle = 91/4 square inches
Area of dilated rectangle = 22.75 square inches
To find out how many times greater the area of the original rectangle is compared to the dilated rectangle, we divide the area of the original rectangle by the area of the dilated rectangle:
Area ratio = (Area of original rectangle) / (Area of dilated rectangle)
Area ratio = 364 square inches / 22.75 square inches
Area ratio ≈ 16 times
Therefore, the area of the original rectangle is 16 times greater than the area of the dilated rectangle.