Question

A $5m60cm$ high vertical pole casts a shadow $3m20cm$ long. Find at the same time the length of the shadow cast by another pole $10m50cm$ high.

Answer 1

Let $xm$ be the length of shadow of the pole whose height is $10m50cm$.

So, $AB=5m60cm=5.60m$ and $BC=3m20cm=2.20m$

Since, the above two triangles are similar as we are measuring at the same time.

So, the corresponding sides are in proportion.

Clearly, it is a case of direct variation.

$\Rightarrow \frac{AB}{BC}=\frac{PQ}{QR}$

$\Rightarrow \frac{5.60}{3.20}=\frac{10.50}{x}$

$\Rightarrow x=\frac{10.50\times 3.20}{5.60}$

$\therefore x=6$

Hence, the length of the shadow is $6m$.