Question

If a girl $1.2$ meters tall casts a shadow $2$ meters long, how many meters tall is a tree that casts a shadow $75$ meters long at the same time?

Answer 1

Hint: In this question, we have to compare a girl and a tree in the terms of shadow and height. So, we will use the concept of equivalent fraction for this purpose.
We will write the individual value of each information.
Then, we will convert the given information into the fraction and put them in the following formula:
Using the formula,
$\dfrac{h}{S} = \dfrac{H}{M}$

Complete step-by-step solution:
First, we understand the question, a girl was a $1.2$ meters tall, so the height of the girl is defined as,
$h = 1.2$ meters
The girl’s height casts a shadow of $2$ meters, so the shadow of the girl is defined as,
$S = 2$ meters
And that tree casts a shadow of $75$ meters long at the same time, so the shadow of the tree is defined as,
$M = 75$ meters
Finally, the question is how many meters tall is the tree that casts a shadow of $75$ meters long at the same time.
$H = ?$
These values are given the question.
Hence, using the following formula,
$\dfrac{h}{S} = \dfrac{H}{M}$
Where,
$h - $ The height of a girl,
$S - $ The shadow of a girl,
$M - $ The shadow of a tree,
$H - $ The height of a tree.
Now, we will substitute the values of $h,S,M$ in the formula
$\dfrac{{1.2}}{2} = \dfrac{H}{{75}}$
Now, we will find the value of $H$ ,
Shifting the constants to one side of the equation,
$H = \dfrac{{1.2}}{2} \times 75$
Multiplying $1.2 \times 75$ , hence we get,
$H = \dfrac{{90}}{2}$
Divide by $2$ ,we get,
$H = 45$ meters

Hence, the tree that casts a shadow of $75$ meters, has the height of $45$ meters.

Note: In this question, we used the concept of equivalent fractions.
What are equivalent fractions?
Equivalent fractions are those fractions which have different numerators and denominators, but they are still equal. This is because they have the same simplified value.
For example: $\dfrac{1}{2} = \dfrac{3}{6} = \dfrac{{150}}{{300}}$ . All of these fractions are of the form $\dfrac{{1k}}{{2k}}$ .
If you notice, all of these fractions are just another fractional form of $50\% $ .