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)
To find the area of the original rectangle, we multiply the length by the width:
Area = length * width = 13 inches * 28 inches = 364 square inches.
To find the area of the dilated rectangle, we multiply each side by the scale factor of 1/4:
New length = 13 inches * 1/4 = 3.25 inches.
New width = 28 inches * 1/4 = 7 inches.
Area = new length * new width = 3.25 inches * 7 inches = 22.75 square inches.
Finally, to find how many times greater the area of the original rectangle is to the area of the dilated rectangle, we divide the area of the original rectangle by the area of the dilated rectangle:
Area of original rectangle / Area of dilated rectangle = 364 square inches / 22.75 square inches = 16.
Therefore, the area of the original rectangle is 16 times greater than the area of the dilated rectangle.