Year 9 Maths Pythagoras Theorem and Trigonometry

Pythagoras Theorem in 3D

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Questions

Question 1

59637

For this cube of side length \(12 cm\) find, correct to 2 decimal places, the length of \(QS\), the diagonal of the base.

Answer

16.97cm

Worked Solution

\begin{align}
&\text{Let the diagonal be}\ d\\
&d\ \text{is the hypotenuse}\\
&\text{with sides of cubes as other two sides}\\
&\begin{aligned}
d^{2}&=12^{2}+12^{2} \\
d^{2}&=144+144 \\
d^{2}&=288 \\
d&=\sqrt{288} \\
d&=16.970 \ldots \\
d &\approx 16.97 \mathrm{~cm}
\end{aligned}\end{align}

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