Try it yourself
Question
A farmer wants to make two triangular enclosures from a rectangular plot of land as shown.
Calculate the total length of fence he will need.
Use Pythagoras' Theorem to work out the length of the diagonal.
\(d^{2}=43.2^{2}+21.6^{2}\)
\(=1866.42\,\,+\,466.56 \)
\(=2332.8 \)
\(d=\sqrt{2332.8}=48.3\,m\)
Total length of fence \(=43.2\,+\,21.6\,+\,43.2\,+\,21.6\,+\,48.3=177.9\,m\)
Question
The cross-section of a building is in the composite shape of a square and a right angled triangle as shown.
The front wall is \(8\,m\) high and the back wall is \(11.2\,m\) high.
The building has a sloping roof.
Calculate the length (\(d\)) of the sloping roof.
The roof is the hypotenuse of a right-angled triangle.
As the lower part of the building is a square we can deduce the measurements of the triangle to be as shown
\( d^{2}=8^{2}+3.2^{2} \)
\( =64\,+10.24 \)
\( =74.24 \)
\( d=\sqrt{74.24}=8.62\,m\)