Use the Pythagorean theorem to find the length of the unknown side of the right triangle. Give an exact answer.
-
A)18
B)25
C)20
D)24

Question

Use the Pythagorean theorem to find the length of the unknown side of the right triangle. Give an exact answer.
-
A)18 
B)25 
C)20 
D)24

Quizplus · Accepted Answer

Based on the image, we can see that the sides of the triangle are in a ratio of 3:4:5. The longest side (hypotenuse) has a length of 12, which is a multiple of 4 (4 x 3). Therefore, we can conclude that the other leg has a length of 3 x 4 = 12. The unknown side is the remaining side, which can be found using the Pythagorean theorem:

a^2 + b^2 = c^2

We know that c = 12 and one leg (b) = 9.

a^2 + 9^2 = 12^2

a^2 + 81 = 144

a^2 = 63

a = sqrt(63)

a = 3(sqrt(7))

Therefore, the length of the unknown side is 3(sqrt(7)). The best choice is C. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse). In this case, we have a right triangle with sides of length 16 and 12. Using the theorem, we can find the length of the unknown side as follows:

a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.
16^2 + 12^2 = c^2
256 + 144 = c^2
400 = c^2
c = √400
c = 20

Therefore, the length of the unknown side is 20, so the answer is C.

Use the Pythagorean Theorem to Find the Length of the Unknown