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Right-angled Triangles, SM-Bank 024

Use Pythagoras' Theorem to decide if the triangle below is right-angled.  (2 marks)

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\(\text{See worked solution}\)

\(\text{The triangle is not right-angled as the sides do not form a Pythagorean triad.}\)

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\(\text{Let }a=19 ,\ b=23\ \text{and }c=24\)

\(\text{Pythagoras’ Theorem states:  }a^2+b^2=c^2\)

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=19^2+23^2\)
    \(=361+529\)
    \(=890\)
    \(\ne 24^2\)
  \(\therefore\ \text{LHS}\) \(\ne \text{RHS}\)

\(\therefore\ \text{The triangle is not right-angled as the sides do not form a Pythagorean triad.}\)