How does the length of the hypotenuse relate to the length of the legs?

1 Answer
mason m
Jan 3, 2016

The relation is called the Pythagorean Theorem. In any right triangle, the following relation is true:

#a^2+b^2=c^2#

where #a# and #b# are the legs (shorter sides) of a right triangle and #c# is the hypotenuse (the longest side, which is opposite the right angle).

For example, a triangle with sides #3,4# and #5# can be shown to be a right triangle.

The legs of the triangle are #3# and #4#, so #a=3# and #b=4#. The longest side of the triangle, #5#, is the hypotenuse, so #c=5#.

#a^2+b^2=c^2#
#3^2+4^2=5^2#
#9+16=25#
#25=25#

lrd.kangan.edu.au

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