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Right-angled Triangles, SM-Bank 047

Use Pythagoras' Theorem to calculate the length of the diagonal in the rectangle below, correct to 1 decimal place.  (2 marks)

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\(8.4\ \text{centimetres}\ (1\ \text{d.p.})\)

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

\(\text{Let }a=4.2\ \text{and }b=7.3\)

\(\text{Then}\ \ c^2\) \(=4.2^2+7.3^2\)
\(c^2\) \(=70.98\)
\(c\) \(=\sqrt{70.98}\)
\(c\) \(=8.4219\dots\approx 8.4\ (1\ \text{d.p.})\)

 
\(\text{The length of the string is }8.4\ \text{centimetres}\ (1\ \text{d.p.})\)