Pythagoras theorem

Question

A factory producing 55-inch LCD screens has placed an order for boxes to contain the screens The width of the screen is 48.5 inches. Given that LCD screens are measured across the diagonal, ie the length of the diagonal is 55 inches, determine if a box with a width of 51 inches and a height of 24 inches will fit a 55-inch LCD screen.

Answer 1

If the width of the 55 inch diagoanal TV is 44.5 inches, and the height is h, then, since the two sides make a right angle between them (and since the TV is a rectangle in shape), we can write

diagonal^2 = height^2+width^2, or,

55^2 = h^2 + 44.5^2

Subtracting 44.5^2 from both sides, we get

55^2 - 44.5^2 = h^2

Applying the equality a^2-b^2 = (a+b)*(a-b), we can resolve the left hand side of the above equation to be

(55+44.5)*(55-44.5) = h^2

or 99.5*10.5 = h^2

or h = Square root of (99.5*10.5) ~ 32.4 inches

So, any box that has to fit the TV must have a width greater than 44.5 inches and height greater than 32.4 inches.

The given box width is 48.5 inches, which is greater than the TV width of 44.5 inches. HOWEVER, the height of the box is 24 inches, which is LESS than the required height of 32.4 or more. So, the TV will not fit inside the given box.

Answer 2