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Rectangle Diagonal

Also known as diagonal of a rectangle · TV screen size · screen diagonal

d=l2+w2d = \sqrt{l^2 + w^2}

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The diagonal is the hypotenuse of the rectangle's two halves, so d=l2+w2d = \sqrt{l^2 + w^2}. Screen sizes are quoted this way — a "55-inch" television measures 55 inches corner to corner, not across — which is why a 16:9 55-inch set is about 48 in wide and 27 in tall. Movers use the same formula to know whether a sheet of plywood will swing through a stairwell.

Two integer solutions show up often enough to memorise: 3-4-5 and 5-12-13. A rectangle 12 in by 5 in has exactly a 13 in diagonal, no rounding — the kind of tidy triple the Babylonians were already tabulating on clay tablet Plimpton 322 well before Pythagoras was born.

Rectangle Diagonal
d=l2+w2d = \sqrt{l^2 + w^2}
Where
  • dd= Diagonal
  • ll= Length
  • ww= Width
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