Question

Tanya wants to buy a flat screen television that will just fit into the space in her entertainment center. The dimensions of the opening where the television would sit are width equal to 37 inches and height equal to 21 inches. Knowing that television sizes are named by the measure of the screen's diagonal, what is the biggest size television she can get that will fit?

Answer 1

Using the Pythagorean theorem, we can find the biggest size television that will fit in Tanya's entertainment center.

Step-by-step explanation:

To find the biggest size television that will fit in Tanya's entertainment center, we need to use the Pythagorean theorem. The diagonal of the television screen is the hypotenuse of a right triangle formed by the height and width of the opening. We can use the formula d = √(w^2 + h^2) to find the diagonal, where d is the diagonal length, w is the width, and h is the height. Plugging in the values w = 37 inches and h = 21 inches, we get:

d = √(37^2 + 21^2) = √(1369 + 441) = √1810 = 42.59 inches

Therefore, the biggest size television that will fit is a 42-inch TV.

Answer 2

42"

Step-by-step explanation:

Given: x = 37"

y = 21"

`\boxed{r^2=x^2+y^2}`

r² = 37² + 21²

= 1369 + 441

r = √1810

= 42.54"

Biggest size is 42"