In the diagram above AB 12cm AE 8cm DCl 9cm and...

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In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|

10cm

9cm

8cm

7cm

|AB| = 12 cm; |DC| = 9 cm; |AE| = 8 cm.

\(\Delta\) ABE and \(\Delta\) EDC are similar triangles. Hence,

\(\frac{|AB|}{|DC|} = \frac{|AE|}{|EC|}\)

\(\frac{12}{9} = \frac{8}{|EC|}\)

\(\therefore |EC| = \frac{9 \times 8}{12}\)

= 6 cm