Question

Emily would like to have a screen 40 inches wide and 32 inches high. About what screen size will she need to buy? Round to the nearest whole number."

A) 20 inches

B) 26 inches

C) 50 inches

D) 72 inches

Answer 1

Using the Pythagorean Theorem to calculate the diagonal of a screen with a width of 40 inches and a height of 32 inches, the screen size Emily needs to buy is approximately 51 inches diagonally, which rounds to 50 inches (Option C).

Step-by-step explanation:

To find the screen size that Emily needs to buy, we will calculate the diagonal measurement of the screen using the dimensions provided: 40 inches wide and 32 inches high. This can be done by applying the Pythagorean Theorem (a² + b² = c²), where 'a' and 'b' are the lengths of the screen's width and height while 'c' is the diagonal measurement.

Here is the calculation step-by-step:

1. Substitute the given width (a=40 inches) and height (b=32 inches) into the Pythagorean Theorem equation: 40² + 32² = c².
2. Calculate the squares: 1600 + 1024 = c².
3. Add the results: 2624 = c².
4. Take the square root of 2624 to find 'c': c ≈ 51.23 inches.
5. Round to the nearest whole number: approximately 51 inches.

Therefore, Emily should look for a screen size that is close to 51 inches when measured diagonally, which rounds to the option C) 50 inches.