Question

3) A vertical stick 40 metre long casts a shadow 20 metre long on the ground.
At the same time, a tower of height x metre casts a shadow 50 metre long
on the ground. Find the value of x.​

Answer 1

Step-by-step explanation:

Given:-

A vertical stick 40 metre long casts a shadow 20 metre long on the ground. At the same time, a tower of height x metre casts a shadow 50 metre long on the ground.

To find:-

Find the value of x.

Solution:-

Length of the vertical stick = 40 metres

Length of its shadow = 20 metres

Height of the tower = X metres

Length of its shadow = 50 metres

On converting the above information to diagrams

From the triangles ∆ABC and ∆DEF

AC = DF (Sun rays)

angle ABC = angle DEF=90°

Both are Similar triangles

So The ratio of corresponding sides is in the Proportion

=>AB/DE = BC/EF=AC/DF

=>40/20=X/50

=>2/1 = X/50

=>2 = X/50

=>X = 2×50

=>X = 100 metres

Answer:-

The value of X for the given problem is 100 m

The height of the tower = 100 metres

Used Concept:-

• Two polygons are said to be similar, If
• The corresponding angles are equal.
• The ratio of corresponding sides is equal.