In triangle \(ABC\), angle \(ABC = 90^\circ\), \(AB = 9\) cm and \(BC = 12\) cm. Write down the length of \(AC\).
Question 1 Report
In triangle \(ABC\), angle \(ABC = 90^\circ\), \(AB = 9\) cm and \(BC = 12\) cm.
Write down the length of \(AC\).
Answer Details
The right angle is at \(B\), so the side opposite it, \(AC\), is the hypotenuse and is the longest side of the triangle. "Write down" signals that the answer is expected to be recognised or found in one short step.
By Pythagoras' theorem, \[AC^{2}=AB^{2}+BC^{2}=9^{2}+12^{2}=81+144=225\] \[AC=\sqrt{225}=15\text{ cm}\] [B1] cao
This is the 3, 4, 5 right-angled triangle enlarged by a scale factor of 3, which is worth recognising on sight since it appears constantly. Check the answer is plausible: the hypotenuse must exceed both shorter sides but be less than their sum, and \(9\lt 15\lt 21\). Subtracting instead of adding would give \(\sqrt{63}=7.94\) cm, shorter than one of the other sides, which is impossible for a hypotenuse.
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