Question

If a tree $24m$ high casts a shadow of $15m$, then the height of a pole that casts a shadow of $6m$ under similar conditions is $9.6m$.

State whether the statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Apply condition for direct proportionality

Under similar conditions , the length of the shadow is directly proportional to the height of the object .

Direct proportionality implies, that the ratio of the two heights, that is the ratio of the heights of the pole must be equal to the ratio of the length of the shadows.

Let the height of the pole be $xm$

$\frac{24}{x}=\frac{15}{6}$

$x=24\times \frac{6}{15}=9.6m$

$9.6m$ is the given height of the tower.

Thus the calculated and actual height of the tower is same.

Hence the given statement is true.