Question

In the adjoining figure, $\angle ABC={90}^{\circ }$ and $BD\perp AC$. If AB = 5.7 cm, BD = 3.8 cm, CD = 5.4 cm, then find the length of BC.

• A. 6.1 cm
• B. 4.1 cm
• C. 8.1 cm
• D. 7.1 cm

Answer 1

The correct option is C

8.1 cm

In $\Delta ABCand\Delta BDC$
$\angle ABC=\angle BDC={90}^{\circ }$ (given)
$\angle ACB=\angle DCB$ (common)
We know that when two angles of a triangle is equal to correspoinding angles of the other triangle, then triangles will be similar.
$\therefore \Delta ABC\sim \Delta BDC\Rightarrow \frac{AB}{BD}=\frac{BC}{DC}$
$\frac{5.7cm}{3.8cm}=\frac{BC}{5.4cm}$ [$\because$ AB = 5.7 cm, BD = 3.8 cm, CD = 5.4 cm]
or, $3.8\times BC=5.7\times 5.4$
or, $BC=\frac{5.7\times 5.4}{3.8}=8.1cm$
Hence, the length of BC = 8.1 cm.