Question

A tower of height 24 m casts a shadow of 50 m and at the same time and on the same side a girl of height 1.8 m casts a shadow. The girl's shadow is of length .

• A. 3 m
• B. 3.5 m
• C. 3.75 m

Answer 1

The correct option is C 3.75 m

Let AB be the height of tower, BC be the length of the shadow of the tower, ED be the height of the girl and EC = x be the length of her shadow.

In $△ABC$ and $△DEC$,
$\angle ABC=\angle DEC={90}^{\circ }$
$\angle BCA=\angle ECD$
(common in both triangles)

Therefore, $△ABC\sim △DEC$
(by AA similarity criterion)

$\Rightarrow$ $\frac{DE}{AB}=\frac{EC}{BC}$ (corresponding sides of similar triangles are in same ratio)
$\Rightarrow$ $EC=DE\times \frac{BC}{AB}$

$\Rightarrow$ $EC=1.8\times \frac{50}{24}$

$\Rightarrow EC=3.75m$

Therefore, length of the her shadow is 3.75 m.