Question

Find the value of $x$ in the following figure.

• A. 5cm
• B. 3cm
• C. 4.8cm
• D. 5.2cm

Answer 1

The correct option is C 4.8cm

In a right angled triangle ,if a perpendicular is drawn from the vertex of the right angle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Consider $\Delta BCA$ and $\Delta CDA$
$\angle A$ = $\angle A$ (common angles)
$\angle BCA=\angle CDA$ (Right angles)

$\therefore \Delta BCA\sim \Delta CDA$

$\to \frac{BC}{CD}=\frac{AB}{AC}$

$\to \frac{6}{x}=\frac{10}{8}$

$\to x=\frac{48}{10}=4.8cm$
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