Question 90

Line segment AB is parallel to line segment CD. AD intersects BC in E. If lengths of AE, BC and ED are 12 cm, 12 cm and 18 cm respectively, what is the length of EC?

Solution

BC = 12 cm, => BE = (12 - x) cm

AB is parallel to CD, => $$\angle$$ BAE = $$\angle$$ CDE and $$\angle$$ ABE = $$\angle$$ DCE

=> $$\triangle$$ABE $$\sim$$ $$\triangle$$ CDE

=> $$\frac{AE}{DE} = \frac{BE}{CE}$$

=> $$\frac{12}{18} = \frac{12 - x}{x}$$

=> $$\frac{2}{3} = \frac{12 - x}{x}$$

=> $$2x = 36 - 3x$$

=> $$x = \frac{36}{5} = 7.2$$ cm

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