Question

A girl $5.5$ feet casts a shadow $70$ inches long. At the same time a telephone pole casts a shadow $314$ inches long. Which proportion cannot be used to find the height of the telephone pole ?

• A. $\left(\frac{70}{5.5}\right)=\left(\frac{314}{x}\right)$
• B. $\left(\frac{70}{314}\right)=\left(\frac{5.5}{x}\right)$
• C. $\left(\frac{x}{5.5}\right)=\left(\frac{314}{70}\right)$
• D. $\left(\frac{70}{x}\right)=\left(\frac{5.5}{314}\right)$

Answer 1

The correct option is D $\left(\frac{70}{x}\right)=\left(\frac{5.5}{314}\right)$

At the same time, position of sun will be fixed for both, hence the angle subtended by shadow on the tip of telephone cast will be the same as that of shadow on the head of girl.

Let $x$ be height of telephone cast in feet.

$\therefore \frac{x}{314}=\frac{5.5}{70}$

$\Rightarrow$ D is incorrect.