Question

One of the legs of a right triangle measures 9 cm and the other leg measures 11 cm.

Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

Answer 1

`\boxed {\boxed {\sf 14.2 \ cm}}`

Explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.

`a^2+b^2=c^2`

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:

• a= 9 cm
• b= 11 cm

Substitute these values into the formula.

`(9 \ cm)^(2) +(11 \ cm)^(2) =c^(2)`

Solve the exponents.

• (9 cm)²= 9 cm*9 cm=81 cm²

`81 \ cm^(2) +(11 \ cm)^(2) =c^(2)`

• (11 cm)²= 11 cm*11 cm= 121 cm²

`81 \ cm^(2) +121 cm^(2) =c^(2)`

Add the values on the left side.

`202 \ cm^(2) =c^(2)`

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.

`\sqrt {202 \ cm^(2) }=\sqrt{c^(2) }`

`\sqrt {202 \ cm^(2) }=c`

`14.2126704036 \ cm =c`

We are told to round to the nearest tenth.

• 14.2126704036

The 1 in the hundredth place tells us to leave the 2 in the tenth place.

`14.2 \ cm= c`

The hypotenuse is equal to 14.2 centimeters.