Question

10 abd and abc are right - angled triangles.
find the length of cd
give your answer correct to 3 significant figures.
ab = 16cm bc = 12cm ad = 1.5×ac

Explanation:

Step1: Find the length of \(AC\) using the Pythagorean theorem in \(\triangle ABC\)

In right - angled triangle \(ABC\) with \(AB = 16\mathrm{cm}\) and \(BC = 12\mathrm{cm}\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the hypotenuse), we have \(AC=\sqrt{AB^{2}+BC^{2}}\).

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Step2: Find the length of \(AD\)

Given \(AD = 1.5\times AC\). Substitute \(AC = 20\mathrm{cm}\) into the equation. Then \(AD=1.5\times20 = 30\mathrm{cm}\)

Step3: Find the length of \(CD\)

Since \(CD=AD - AC\), and \(AD = 30\mathrm{cm}\), \(AC = 20\mathrm{cm}\)
\(CD=30 - 20=10.0\mathrm{cm}\)

Answer:

\(10.0\mathrm{cm}\)