Similarity, SMB-026

The two triangles below are similar.

Find the length of \(ED\). (3 marks)

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\(ED = 15\)

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\(\text{Using Pythagoras in}\ \Delta ABC: \)

\( AB=\sqrt{13^2-12^2}=\sqrt{25}=5 \)

\(\text{Scale factor}\ = \dfrac{FD}{AC} = \dfrac{39}{13} = 3 \)

\(\therefore ED = 3 \times AB = 3 \times 5 = 15 \)