Question

a square poster of length 3x is going to have a square painting centered on it. The length of the painting is 2x. the area of the poster not covered by the painting will be painted black. what is the area of the poster that will be painted black?

Answer 1

To calculate the area that will be painted black on the poster, subtract the area of the painting (4x^2) from the area of the poster (9x^2) resulting in 5x^2.

Step-by-step explanation:

To determine the area of the poster that will be painted black, we need to find the areas of both the poster and the painting, and then subtract the area of the painting from the area of the poster.

The area of the poster is given by the formula for the area of a square, which is side length squared. Therefore, the area of the poster is (3x)^2 or 9x^2.

The area of the painting, which is also a square, is given by (2x)^2 or 4x^2.

Subtracting the area of the painting from the poster, we get 9x^2 - 4x^2, which equals 5x^2. This is the area of the poster that will be painted black.

As an example, if we consider Marta's case who has one square with a side length of 4 inches, we can compare it to a similar square with dimensions twice the first square. The area of this larger square will be 4 times larger than that of the smaller square because the ratio of areas of similar figures is the square of the scale factor.

Answer 2

One way to solve this is to look at the size of the poster, and then subtract the size of the picture so you have the area that needs to be painted left.

Area of square poster - 3x × 3x = 9x^2
Area of painting - 2x × 2x = 4x^2

9x^2 - 4x^2 = 5x^2

The area is 5x^2