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In a right triangle, side a is 3 times as long as side b, and side c is 30 cm. Using the Pythagorean Theorem, what are the lengths of sides a and b? Round your answers to the nearest tenth.

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Answer:

a = 9√10

b=3√10

Step-by-step explanation:

see attached for reference for any right triangle

in our case

c is the hypotenuse

hence

c² = a² + b²

we are given that c = 30

also that a is 3 times as long as b or,

a = 3b    

substituting these into the pytharogrean formula.

c² = a² + b²

30² = (3b)² + b²

900 = 9b²+b²

10b² = 900

b² = 90

b = √90 = √9 √10 = 3√10

earlier we found that a = 3b,

hence

a = 3(3√10)

a = 9√10

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