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Trigonometry
Question

Triangle \( A B C \) has side lengths \( 9,40 , \)...

Triangle \( A B C \) has side lengths \( 9,40 , \) and \( 41 . \) Do the side lengths form a Pythagorean triple? Explain. 

a Yes, they form a Pythagorean triple; \( 9 ^ { 2 } + 40 ^ { 2 } = 41 ^ { 2 } \) and \( 9,40 \) , and \( 41 \) are all nonzero whole numbers.

 b No, they do not form a Pythagorean triple; \( 9 ^ { 2 } + 40 ^ { 2 } \neq 41 ^ { 2 } \) . 

c No, they do not form a Pythagorean triple; although \( 9 ^ { 2 } + 40 ^ { 2 } = 41 ^ { 2 } \) , the side lengths do not meet the other requirements of a Pythagorean triple. 

d.Yes; they can form a right triangle, so they form a Pythagorean triple. 

Answer

Pythagorean triple

\(largestside^ 2 = shortestside^ 2+ secondshortestside^ 2\)

given sides 9,40,41

\(41^ 2 = 1681\\ 40^ 2= 1600\\ 9^ 2= 81\\ 41^ 2= 40^ 2+ 9^ 2\\ so they are pytagorean triple\)

 

Answer: Option A)

Solution
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