What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 7 and 1?

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Answer 1 · 2015-12-21T01:23:19

The length of the hypotenuse is #5sqrt 2#.

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

Substitute #7# and #1# into the equation for #a and b#.

#c^2=7^2+1^2#

Simplify.

#c^2=49+1#

Simplify.

#c^2=50#

Take the square root of both sides.

#c=sqrt50#

Factor #sqrt 50#.

#c=sqrt(2xx5xx5)#

Simplify.

#c=sqrt (2xx5^2)#

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

#c=5sqrt2#