Answer:
3.60555128 cm or √13 cm
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse.
We know the shorter legs are 2 cm and 3 cm. We don't know the hypotenuse.
[tex]a=2\\b=3[/tex]
Substitute the values into the formula.
[tex]2^2+3^2=c^2[/tex]
Evaluate the exponents.
⇒2²=2*2=4
[tex]4+3^2=c^2[/tex]
⇒3²=3*3=9
[tex]4+9=c^2[/tex]
Add 4 and 9.
[tex]13=c^2[/tex]
c is being squared. The inverse of a square is the square root. Take the square root of both sides of the equation.
[tex]\sqrt{13} =\sqrt{c^2}[/tex]
[tex]\sqrt{13}=c[/tex]
[tex]3.60555128=c[/tex]
Add units, in this case centimeters, or cm.
[tex]c=3.60555128 cm[/tex]
The length of the hypotenuse is 3.60555128 or √13 centimeters.
