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QuestionFind the hypotenuse of a right triangle with sides 12 and 8. Options: A) 12.7 B) 208 C) 14.4 D) 16.5.

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. One side of the triangle has a length of123. Another side of the triangle has a length of84. We are looking for the length of the hypotenuse

STEP 2

We can use the Pythagorean theorem to find the length of the hypotenuse in a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written asc2=a2+b2c^2 = a^2 + b^2where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

STEP 3

Now, plug in the given values for the lengths of the two sides into the Pythagorean theorem.
c2=122+82c^2 =12^2 +8^2

STEP 4

Calculate the squares of the lengths of the two sides.
c2=144+64c^2 =144 +64

STEP 5

Add the squares of the lengths of the two sides.
c2=208c^2 =208

STEP 6

To find the length of the hypotenuse (c), we need to take the square root of both sides of the equation.
c=208c = \sqrt{208}

STEP 7

Calculate the square root of208.
c=14.4c =14.4So, the length of the hypotenuse is14.4, which corresponds to option C.

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