HELP ME ON MY PRE CALC REVIEW

Question

In a standard television set, the screen height is 0.75 times the screen width. If a television set measures 24 inches along the diagonal, what is the screen width in inches ?

Answer 1

Let w be the width of the screen. Then, the height of the screen is h = 0.75w. Moreover, we have w^2 + h^2 = d^2, where d is the length of the diagonal of the screen. Plugging in the appropriate values into this equation gives us w^2 + (0.75w)^2 = 24^2. Simplifying, we have w^2 + 0.5625w^2 = 576. Combining like terms gives 1.5625w^2 = 576. Dividing both sides by 1.5625 yields w^2 = 368.64. Finally, taking the square root of both sides, we have w= 19.2, so the width of the screen is 19.2 inches.