smc

Question

Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3. The horizontal length of a "27-inch" television screen is closest, in inches, to which of the following?

Accepted Answer

If you divide the television screen into two right triangles, the legs are in the ratio of 4 : 3, and we can let one leg be 4x and the other be 3x. Then we can use the Pythagorean Theorem. align*(4x)^2+(3x)^2&=27^2 16x^2+9x^2&=729 25x^2&=729 x^2&=72925 x&=275 x&=5.4align* The horizontal length is 5.44=21.6, which is closest to 21.5.