Question

A $25$ foot building casts a $6$ foot shadow. How tall is the building that casts a $24$ foot shadow at the same time?

Answer 1

Hint: First, we have to write down the information in the form of diagram and analyse that in the table such that it is proportional to each other. Then doing some cross multiply and such simplification we get the required answer.

Complete step-by-step solution:
First, let us understand the question using a diagram representation.
A $25$ foot building casts a $6$ foot shadow. The vertical line denotes the height of the building and the horizontal line denotes the shadow it casts.

Now, with this diagram we will draw the building that casts a $24$ foot shadow at the same time.

Now, we have to find the h.
Since the diagrams are the same in nature, it has to be proportionate to each other.
We can clearly see that the height and shadow of the two buildings are proportionate to each other.
When the given details are proportionate, we can find the required value easily.

	$1$	$2$
Height	$25$	$h$
Shadow	$6$	$24$

By cross multiplying, we can find the ${\text{h}}$
$\dfrac{{25}}{6} = \dfrac{{\text{h}}}{{24}}$
On doing cross multiplying and we can write it as,
$25 \times 24 = {\text{h}} \times {\text{6}}$
Let us multiply the term and we get
${\text{h}} \times {\text{6 = 600}}$
Transferring $6$ to the other side,
${\text{h = }}\dfrac{{600}}{6}$
On dividing we get
${\text{h = 100}}$ foot

Therefore, the building that casts a $24$ foot shadow is $100$ foot tall.

Note: To understand such types of questions without any mistakes, always try to draw a rough diagram of the problem given.
Proportionate to each other means that their corresponding angles are congruent and so their sides.
Alternative method of solving:
It is given that a$25$ foot building casts a $6$ foot shadow.
Therefore for one foot shadow, the building’s height will be = $\dfrac{{25}}{6}$
Given that, a building casts a $24$ foot shadow
Therefore for $24$ foot shadow, the building’s height will be =$\dfrac{{25}}{6} \times 24$
The height is ${\text{ }}\dfrac{{600}}{6} = 100$ foot.