Question

You buy a new television with a screen similar in shape to your old television screen, but with an area four times greater. The size of a television screen is often described using the distance between opposite corners of the screen. Your old television has a 30-inch screen. What is the size of your new television screen? Explain.

Answer 1

The size of the new television screen is 120 square inches and 60 inches in diagonal.

Step-by-step explanation:

To find the size of the new television screen, we need to use the concept of area. If the old television screen has an area of 30 square inches, and the new television has an area four times greater, then the area of the new television screen is 30 x 4 = 120 square inches.

The size of a television screen is often described using the distance between opposite corners, which is called the diagonal. To find the diagonal of the new television screen, we can use the concept of similar triangles. Since the area of the new screen is four times greater, the linear dimensions (height and width) of the new screen are two times greater. Therefore, the diagonal of the new television screen is also two times greater.

The diagonal of the old television screen is 30 inches, so the diagonal of the new television screen is 30 x 2 = 60 inches.