Answer:
The lenght of the hypotenuse is \(\sqrt{250}\) units or \(15.811\) units.
Step-by-step explanation:
We are going to use the Pythagorean theorem to solve this.
The Pythagorean theorem states that given a right triangle in which ''a'' and ''b'' are the length of the legs and ''c'' is the length of the hypotenuse, this three lengths satisfy the following equation :
\(a^{2}+b^{2}=c^{2}\)
To find the length of the hypotenuse in this exercise, we need to replace the values \(a=5units\) and \(b=15units\) in the equation and then find the value of c that satisfy it ⇒
\((5units)^{2}+(15units)^{2}=c^{2}\)
\(25(units)^{2}+225(units)^{2}=c^{2}\)
\(250(units)^{2}=c^{2}\)
Given that \(c>0\) ⇒
\(c=\sqrt{250(units)^{2}}\)
\(c=\sqrt{250}units\)
or \(c=15.811units\)
