Acertain television is advertised as a 40-inch tv (the diagonal length). if the width of the tv is 24 inches, how many inches tall is the tv?

Here applies the Pitagora Theorem!

You make a traingle out of the tv. One side is the 40 inch diagonal, anothet is the base of the triangle(the tv's width) of 24 inches and the height is the third side of the triangle which is X. The theorem says that square 40 inch = square X + square 24.
1600= square X + 576 where square X is 1024 so Just X = root 1024 which is 32.
X=32 inches tall (hight of the tv)