Please help me to understand. I have a similar homework problem to this one I am posting. If you have a square television with a diagonal of 49" what is the measurement of one side? I am just not getting it. Thank you for any help.

The hypotenuse of an isosceles right triangle (half of a square) is the length of either of the two sides multiplied by the square root of two. Use the reciprocal to calculate the length of the sides from the hypotenuse. I don't recall seeing a TV that is actually square though.

American analog TVs and older computer displays are a mathematically convenient 3:4 ratio. A twenty inch display (lets assume it's an LCD with straight edges) would be 12 X 16 (4X5 hypotenuse 4X3 and 4X4 sides). Many of the newer TVs have a 16:9 side length ratio. The ratio between the diagonal measurement and the height (or between the diagonal and the width) would always be the same, so once you calculate that ratio for a 16 by 9 display you can use that ratio (or a reciprical) to calculate the height and width for other screen sizes. That consistency is the basis for trigonometric ratios (sine, cosine, tangent etc)

The square of one is one. Twice one is two. The hypotenuse of the isosceles right triangle is therefore the square root of two

The square of three is nine. The square of four is sixteen. It's easy to calculate the square root of their sum.

Find the square root of the sum of nine squared plus sixteen squared to determine the diagonal measurement of a 16X9 rectangle.