What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 2 and 16?

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Answer 1 · 2015-12-28T01:45:04

#c=2sqrt65#

Use the Pythagorean theorem, #c^2=a^2+b^2#, where #c# is the hypotenuse, and #a# and #b# are the other two sides.

Let side #a=2# and side #b=16#.

Substitute the given values into the equation.

#c^2=2^2+16^2#

Simplify.

#c^2=4+256#

Simplify.

#c^2=260#

Take the square root of both sides.

#c=sqrt260#

Determine the prime factors of #260#.

#c=sqrt(2xx2xx5xx13)#

Group identical factors.

#c=sqrt((2xx2)xx5xx13)#

Rewrite #(2xx2)# as #2^2#.

#c=sqrt(2^2xx5xx13)#

Apply the square root rule #sqrt(a^2)=a#.

#c=2sqrt(5xx13)#

Simplify.

#c=2sqrt65#