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

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

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

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

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

Right-angled Triangles, SM-Bank 023

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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\(\text{Let }a=7 ,\ b=15\ \text{and }c=17\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=7^2+15^2\)
    \(=49+225\)
    \(=274\)
    \(\ne 17^2\)
  \(\therefore\ \text{LHS}\) \(\ne \text{RHS}\)

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

Right-angled Triangles, SM-Bank 022

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

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\(\text{See worked solution}\)

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

Show Worked Solution

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

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

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

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

Right-angled Triangles, SM-Bank 021

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

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\(\text{See worked solution}\)

\(\text{The triangle is right-angled as the sides form a Pythagorean triad.}\)

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\(\text{Let }a=13 ,\ b=84\ \text{and }c=85\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=13^2+84^2\)
    \(=169+7056\)
    \(=7225\)
    \(=85^2\)
    \(=\text{RHS}\)

\(\therefore\ \text{The triangle is right-angled as the sides form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 020

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

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\(\text{See worked solution}\)

\(\text{The triangle is right-angled as the sides form a Pythagorean triad.}\)

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\(\text{Let }a=1.5 ,\ b=2\ \text{and }c=2.5\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=1.5^2+2^2\)
    \(=2.25+4\)
    \(=6.25\)
    \(=2.5^2\)
    \(=\text{RHS}\)

\(\therefore\ \text{The triangle is right-angled as the sides form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 019

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

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\(\text{See worked solution}\)

\(\text{The triangle is right-angled as the sides form a Pythagorean triad.}\)

Show Worked Solution

\(\text{Let }a=24 ,\ b=7\ \text{and }c=25\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=24^2+7^2\)
    \(=576+49\)
    \(=625\)
    \(=25^2\)
    \(=\text{RHS}\)

\(\therefore\ \text{The triangle is right-angled as the sides form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 018

Use Pythagoras' Theorem to decide if the numbers \(7, 8\) and \(11\) form a Pythagorean triad.  (2 marks)

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\(\text{See worked solution}\)

\(7,\ 8\ \text{and }11\ \text{do not form a Pythagorean triad.}\)

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\(\text{Let }a=7 ,\ b=8\ \text{and }c=11\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=7^2+8^2\)
    \(=49+64\)
    \(=113\)
    \(\ne 11^2\)
  \(\therefore\ \ \) \(\ne\text{RHS}\)

\(\therefore\ 7,\ 8\ \text{and }11\ \text{do not form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 017

Use Pythagoras' Theorem to decide if the numbers \(1.4, 4.8\) and \(5.2\) form a Pythagorean triad.  (2 marks)

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\(\text{See worked solution}\)

\(1.4,\ 4.8\ \text{and }5.2\ \text{do not form a Pythagorean triad.}\)

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\(\text{Let }a=1.4 ,\ b=4.8\ \text{and }c=5.2\)

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

\(\text{LHS: }\rightarrow\ \) \(a^2+b^2\) \(=1.4^2+4.8^2\)
    \(=1.96+23.04\)
    \(=25\)
    \(=5^2\ne\text{RHS}\)

\(\therefore\ 1.4,\ 4.8\ \text{and }5.2\ \text{do not form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 016

Use Pythagoras' Theorem to decide if the numbers \(36, 48\) and \(63\) form a Pythagorean triad.  (2 marks)

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\(\text{See worked solution}\)

\(36,\ 48\ \text{and }63\ \text{do not form a Pythagorean triad.}\)

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\(\text{Let }a=36 ,\ b=48\ \text{and }c=63\)

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

\(\text{LHS: }\longrightarrow\ \) \(a^2+b^2\) \(=36^2+48^2\)
    \(=1296+2304\)
    \(=3600\)
    \(=60^2\ne\text{RHS}\)

\(\therefore\ 36,\ 48\ \text{and }63\ \text{do not form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 015

Use Pythagoras' Theorem to decide if the numbers \(1.1 ,\ 6\) and \(6.1\) form a Pythagorean triad.  (2 marks)

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\(\text{See worked solution}\)

\(1.1,\ 6\ \text{and }6.1\ \text{form a Pythagorean triad.}\)

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\(\text{Let }a=1.1 ,\ b=6\ \text{and }c=6.1\)

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

\(\text{LHS: }\longrightarrow\ \) \(a^2+b^2\) \(=1.1^2+6^2\)
    \(=1.21+36\)
    \(=37.21\)
    \(=6.1^2=\text{RHS}\)

\(\therefore\ 1.1,\ 6\ \text{and }6.1\ \text{form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 014

Use Pythagoras' Theorem to decide if the numbers \(12 , 35\) and \(37\) form a Pythagorean triad.  (2 marks)

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\(\text{See worked solution}\)

\(12,\ 35\ \text{and }37\ \text{form a Pythagorean triad.}\)

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\(\text{Let }a=12 ,\ b=35\ \text{and }c=37\)

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

\(\text{LHS: }\longrightarrow\ \) \(a^2+b^2\) \(=12^2+35^2\)
    \(=144+1225\)
    \(=1369\)
    \(=37^2=\text{RHS}\)

\(\therefore\ 12,\ 35\ \text{and }37\ \text{form a Pythagorean triad.}\)

Right-angled Triangles, SM-Bank 013

Use Pythagoras' Theorem to decide if the numbers \(5 , 12\) and \(13\) form a Pythagorean triad.  (2 marks)

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\(\text{See worked solution}\)

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\(\text{Let }a=5 ,\ b=12\ \text{and }c=13\)

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

\(\text{LHS: }\longrightarrow\ \) \(a^2+b^2\) \(=5^2+12^2\)
    \(=25+144\)
    \(=169\)
    \(=13^2=\text{RHS}\)

\(\therefore\ 5,\ 12\ \text{and }13\ \text{form a Pythagorean triad.}\)