Question

# In $$\triangle$$ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.

Solution

## The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.It is given that $$AD=6$$ cm, $$DB=9$$ cm and $$AE=8$$ cm.Using the basic proportionality theorem, we have$$\frac { AD }{ AB } =\frac { AE }{ AC } =\frac { DE }{ BC } \\ \Rightarrow \frac { AD }{ AB } =\frac { AE }{ AC } \\ \Rightarrow \frac { 6 }{ 15 } =\frac { 8 }{ AC } \\ \Rightarrow 6AC=15\times 8\\ \Rightarrow 6AC=120\\ \Rightarrow AC=\frac { 120 }{ 6 } =20$$Hence, $$AC=20$$ cm.Mathematics

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