A rectangle’s diagonal: convert the units before using Pythagoras
Find a right-triangle diagonal and check the result without mixing centimetres and metres.
Method
A rectangle’s width and height form perpendicular sides of a right triangle. Its diagonal is the hypotenuse, opposite the right angle. Convert both sides to one length unit, square them, add, then take the positive square root. Adding the side lengths would measure a route along two edges, not the diagonal.
Worked example
For a panel 1.2 metres wide and 90 centimetres high, enter 1.2 and 0.9 in Pythagorean theorem. The diagonal is 1.5 metres. The equations below show a reverse check: subtract the shorter side’s square from the diagonal’s square and recover the other side.
a = 1.2 m; b = 90 cm = 0.9 m
c = √(1.2² + 0.9²) = √2.25 = 1.5 m
1.5² − 0.9² = 1.44; √1.44 = 1.2 m
Checks and limits
This method requires a right angle. For an arbitrary triangle, two sides alone do not determine the third. The diagonal should be longer than either perpendicular side and shorter than their sum. Measurement uncertainty and rounded inputs carry into the result; this calculation does not establish the structural suitability of a panel.
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Source: OpenStax