Answer:
The lenght of the hypotenuse is [tex]\sqrt{250}[/tex] units or [tex]15.811[/tex] 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 :
[tex]a^{2}+b^{2}=c^{2}[/tex]
To find the length of the hypotenuse in this exercise, we need to replace the values [tex]a=5units[/tex] and [tex]b=15units[/tex] in the equation and then find the value of c that satisfy it ⇒
[tex](5units)^{2}+(15units)^{2}=c^{2}[/tex]
[tex]25(units)^{2}+225(units)^{2}=c^{2}[/tex]
[tex]250(units)^{2}=c^{2}[/tex]
Given that [tex]c>0[/tex] ⇒
[tex]c=\sqrt{250(units)^{2}}[/tex]
[tex]c=\sqrt{250}units[/tex]
or [tex]c=15.811units[/tex]
