Answer:
[tex]\boxed {\boxed {\sf 14.2 \ cm}}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse. In this triangle, we know the legs are 9 centimeters and 11 centimeters, or:
Substitute these values into the formula.
[tex](9 \ cm)^{2} +(11 \ cm)^{2} =c^{2}[/tex]
Solve the exponents.
[tex]81 \ cm^{2} +(11 \ cm)^{2} =c^{2}[/tex]
[tex]81 \ cm^{2} +121 cm^{2} =c^{2}[/tex]
Add the values on the left side.
[tex]202 \ cm^{2} =c^{2}[/tex]
Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.
[tex]\sqrt {202 \ cm^{2} }=\sqrt{c^{2} }[/tex]
[tex]\sqrt {202 \ cm^{2} }=c[/tex]
[tex]14.2126704036 \ cm =c[/tex]
We are told to round to the nearest tenth.
The 1 in the hundredth place tells us to leave the 2 in the tenth place.
[tex]14.2 \ cm= c[/tex]
The hypotenuse is equal to 14.2 centimeters.
