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Right-angled Triangles, SM-Bank 022

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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\(\text{Let }a=6 ,\ b=7\ \text{and }c=8\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=6^2+7^2\)
    \(=36+49\)
    \(=85\)
    \(\ne 8^2\)
  \(\therefore\ \text{LHS}\) \(\ne \text{RHS}\)

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