An electric pole casts a shadow of length 42 m at a time when a tree 12 m high casts a shadow of length 16 m. Find the height of the pole.

Correct option is A

Given

Height of the tree: 12 m

Length of the tree's shadow: 16 m

Length of the pole's shadow: 42 m

Concept Used

The ratio of the height of an object to the length of its shadow remains constant because of the similar triangles formed by the objects and their shadows.

Formula Used

​$$\frac{\text{Height of tree}}{\text{Shadow of tree}} = \frac{\text{Height of pole}}{\text{Shadow of pole}}$$​​

Solution: 

Applying the formula;

​$$\frac{12}{16} = \frac{\text{Height of Tree}}{42} \\ \ \\ \text{Height of Tree} = \frac{12 \times 42}{16} = 31.5 \ m$$​​