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#a# and #b# are the legs of a right triangle. #c# is the hypotenuse. If #c=13, b=2a#, what is #a# and #b#?

1 Answer

Feb 26, 2017

#a=(13sqrt5)/5#
# b=(26sqrt5)/5#

Explanation:

By Pythagorean Theorem, we know that:

#c^2=a^2+b^2#, where #c# is the hypotenuse and #a and b# are the legs.

Given that #c=13, and b=2a#,

#=> 13^2=a^2+(2a)^2#
#=> 13^2=a^2+4a^2#
#=> 13^2=5a^2#,
#=> a^2=13^2/5#
#=> a=13/sqrt5=(13sqrt5)/5#

#=> b=2a=2xx(13sqrt5)/5=(26sqrt5)/5#

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