Question

copy and solve determine whether each triangle is a right triangle. justify your answer. show your work on a separate piece of paper. 18. 24 m, 143 m, 145 m 19. 135 in., 140 in., 175 in. 20. 56 ft, 65 ft, 16 ft 21. 44 cm, 70 cm, 55 cm

Explanation:

Step1: Apply Pythagorean theorem

For a triangle with side lengths \(a\), \(b\), \(c\) (\(c\) is the longest side), check if \(a^{2}+b^{2}=c^{2}\)

Step2: Check problem 18

Let \(a = 24\), \(b=143\), \(c = 145\)
\(a^{2}+b^{2}=24^{2}+143^{2}=576 + 20449=21025\)
\(c^{2}=145^{2}=21025\)
Since \(a^{2}+b^{2}=c^{2}\), it is a right - triangle

Step3: Check problem 19

Let \(a = 135\), \(b = 140\), \(c=175\)
\(a^{2}+b^{2}=135^{2}+140^{2}=18225+19600 = 37825\)
\(c^{2}=175^{2}=30625\)
Since \(a^{2}+b^{2}
eq c^{2}\), it is not a right - triangle

Step4: Check problem 20

Let \(a = 16\), \(b = 56\), \(c = 65\)
\(a^{2}+b^{2}=16^{2}+56^{2}=256+3136 = 3392\)
\(c^{2}=65^{2}=4225\)
Since \(a^{2}+b^{2}
eq c^{2}\), it is not a right - triangle

Step5: Check problem 21

Let \(a = 44\), \(b = 55\), \(c = 70\)
\(a^{2}+b^{2}=44^{2}+55^{2}=1936 + 3025=4961\)
\(c^{2}=70^{2}=4900\)
Since \(a^{2}+b^{2}
eq c^{2}\), it is not a right - triangle

Answer:

1. Yes, it is a right triangle because \(24^{2}+143^{2}=145^{2}\)
2. No, it is not a right triangle because \(135^{2}+140^{2}

eq175^{2}\)

1. No, it is not a right triangle because \(16^{2}+56^{2}

eq65^{2}\)

1. No, it is not a right triangle because \(44^{2}+55^{2}

eq70^{2}\)