A rectangular television screen has a width of 12 inches and a diagonal of 13 inches. find the height of the television?

The height, width and diagonal form a right triangle there. As per Pythagoras's theorem, the sum of the squares of the other two sides is equal to the square of the hypotenuse. Here, hypotenuse is the diagonal (the side opposite to the right angle) and the other two sides are the width and the height. Let the height be x. By Pythagoras Theorem, x^2 + 13^2 = 13^2 x^2 = 13^2 - 12^2 x^2 = 169 - 144 x^2 = 25 x = sqrt 25 = 5 inches

That's a pretty weird television, with a really wide screen and barely any height... but I forget this is Mathworld where we don't have to match reality. The width, height and diagonal form a right triangle. The measures of these sides are related by the Pythagorean Theorem: a² + b² = c² If you remember some common Pythagorean Triples like 3-4-5 and 5-12-13, then you know the answer already... but let's not skip ahead. Stated another way in terms of height, width and diagonal: h² + w² = d² We know: width (w) = 12 inches diagonal (d) = 13 inches h² + 12² = 13² h² + 144 = 169 h² = 169 - 144 h² = 25 h = √25 h = 5 inches Answer: The height is 5 inches

fool ....impossible.....

The diagonal is the hypotenuse of a right triangle formed by the width and height. The square of the hypotenuse is the sum of the squares of the other two sides: 13^2 = 12^2 + h^2 Square the values: 169 = 144 + h^2 Subtract 144 from both sides: 25 = h^2 Take the square roots and flip it around: h = 5 The height is 5 inches.

Pythagorean Theorem. height² + width² = diagonal² height² = 13² - 12²