Question

what is the length, in feet, of the hypotenuse of a right triangle with legs that measure 7 feet and 11 feet, respectively?
a ( 3sqrt{2} )
b ( 6sqrt{2} )
c ( sqrt{170} )
d 18
e ( 18+sqrt{170} )

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 7\) and \(b=11\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So, \(c^{2}=7^{2}+11^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(7^{2}=49\) and \(11^{2}=121\). Then \(c^{2}=49 + 121\).
\(c^{2}=170\).

Step3: Solve for \(c\)

Take the square root of both sides. \(c=\sqrt{170}\) (since \(c>0\) as it represents the length of a side of a triangle).

Answer:

C. \(\sqrt{170}\)