Question

A 36-foot-tall tree casts a 9-foot shadow. How tall is a nearby tree that casts a 14-foot shadow at the same time?

Answer 1

Answer:

Proportion states that the two fractions or ratios are equal.

Given the statement: A 36-foot-tall tree casts a 9-foot shadow.

To find the height of the nearby tree that cast a 14 foot shadow at the same time.

Let x be the height of the nearby tree.

By definition of proportion;

$\frac{\text{Height of thetall tree}}{\text{Shadow of the tall tree}} =\frac{\text{Height of the nearby tree}}{\text{Shadow of the nearby tree}}$

Substitute the given values we get;

$\frac{36}{9}=\frac{x}{14}$

Simplify:

$4 = \frac{x}{14}$

Multiply both sides by 14 we get;

$x= 4 \times 14 = 56$ foot.

therefore, the height of the nearby tree is, 56 foot.