In the given figure, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

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Solution

It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse.

$In △ B D C and △ A B C, we have : ∠ A B C = ∠ B D C = 90 ° (given) ∠ C = ∠ C (common) By AA similarity theorem, we get : △ B D C ~ △ A B C$

$\frac{A B}{B D} = \frac{B C}{D C} \Rightarrow \frac{5.7}{3.8} = \frac{B C}{5.4} \Rightarrow B C = \frac{5.7}{3.8} \times 5.4 = 8.1$

Hence, BC = 8.1 cm

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