The measure of the diagonal is given for the size of the TV. If the dimensions of a 9 inch screen are 5.5 inches and 7.5 inches, what are the dimensions for 54 inch TV?

Answer 1

The length of the diagonal should be proportional to the length of the sides. Since there is a 6 fold increase in the length of the diagonal (54/9= 6)the sides should also increase by a factor of 6 so the new dimensions will be 5.5x6=33 and 7.5x6=45. This will keep the ratio of the sides the same. You can check to see if this will give you a diagonal of 55 by applying pythagorean theorem to the right triangle with legs of 33 and 45

Answer 2

If we assume that the TVs are similar, then we can set up a similarity statement with the small TV numbers on the top and the large TV numbers on the bottom:

small/large∼9/54∼5.5/x∼7.5/y

Then we look for a scale factor... using multiplication, how do we get from the small dimensions to the big ones? In this case, 9 * 6 = 54, so the scale factor is 6.

Last, take the scale factor and use it to multiply the small dimensions in order to find the matching big ones.

5.5 * 6 = 33

7.5 * 6 = 45