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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.

Sagot :

Sarah06109

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:

  • a= 9 cm
  • b= 11 cm

Substitute these values into the formula.

[tex](9 \ cm)^{2} +(11 \ cm)^{2} =c^{2}[/tex]

Solve the exponents.

  • (9 cm)²= 9 cm*9 cm=81 cm²

[tex]81 \ cm^{2} +(11 \ cm)^{2} =c^{2}[/tex]

  • (11 cm)²= 11 cm*11 cm= 121 cm²

[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.

  • 14.2126704036

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.

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