A square with an area of 4in² is dilated by a factor of 7. What is the area of the dilated square?

Solution:

A square is a rectangle with all sides equal. The square with side x is shown below, has an area of 4 inches².

Area of the square is x² = 4 inches².

x = √4 = 2 inches

Dilation is one of the transformations in geometry. Now as per the problem statement the square is dilated by a factor of 7 which implies that the length of the side of the square is multiplied by 7.

x' = 7(x) = 7(2) = 14 inches

The area of the dilated square will be:

Area of the dilated square = x'² = 14 × 14 = 196 inches².

A square with an area of 4in² is dilated by a factor of 7. What is the area of the dilated square?

Summary:

By dilation of the square implies that the sides of the square are modified by the dilation factor which in this case is 7. The new length therefore became 2 x 7 = 14inches. The area therefore increases to 196 inches².