Question

d. (6, 10)
18.
Tower
Ajay's House
Vijay is trying to find the average height of a tower near his house. He is using the
properties of similar triangles. The height of Vijay's house is 20 m when Vijay's house
casts a shadow 10 m long on the ground. At the same time, the tower casts a shadow 50 m
long on the ground. At the same time, the house of Ajay casts 20 m shadow on the ground.
1 What is the height of the tower?
a 20 m
b. 50 m
C100 m
d. 200 m
1. What will be the length of the shadow of the tower when Vijay's house casts a shadow
of 12 m?
And additional questions in pic please solve all​

Answer 1

Given:

Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay's house is 20 m when Vijay's house casts a shadow 10 m long on the ground. At the same time, the tower casts a shadow 50 m long on the ground. At the same time, the house of Ajay casts a 20 m shadow on the ground.

To find:

What is the height of the tower?

What will be the length of the shadow of the tower when Vijay's house casts a  shadow of 12m

What is the height of Ajay's house?

When the tower cast shadow of 40 m, Same time what will be the length

of the shadow of Ajay's house?

When the tower cast shadow of 40 m, Same time what will be the length

of the shadow of Vijay's house?  

Solution:

The given problems are solved using the following property of the similar triangles:

→ The corresponding sides of two similar triangles are proportional to each other ←

Let,

"AB" → the height of Vijay's house  

"BC" → the length of the shadow of Vijay's house  

"PQ" → the height of the tower

"QR" → the length of the shadow of the tower

"XY" → the height of Ajay's house

"YZ" → the length of the shadow of the tower

Finding the height of the tower:

$\frac{AB}{PQ} = \frac{BC}{QR}$

Substituting AB = 20, BC = 10 & QR = 50

$\implies \frac{20}{PQ} = \frac{10}{50}$

$\implies PQ = \frac{20 \times 50}{10}$

$\implies \boxed{\bold{PQ =100\:m}}$ ← Height of the tower

Finding the length of the shadow of the tower when Vijay's house casts a shadow of 12 m:

$\frac{AB}{PQ} = \frac{BC}{QR}$

Substituting AB = 20, BC = 12 & PQ = 100

$\implies \frac{20}{100} = \frac{12}{QR}$

$\implies QR = \frac{12 \times 100}{20}$

$\implies \boxed{\bold{QR =60\:m}}$ ← The length of the shadow of the tower

Finding the height of Ajay's house:

$\frac{AB}{XY} = \frac{BC}{YZ}$

Substituting AB = 20, BC = 10 & YZ = 20

$\implies \frac{20}{XY} = \frac{10}{20}$

$\implies XY = \frac{20 \times 20}{10}$

$\implies \boxed{\bold{XY = 40\:m}}$ ← Height of Ajay's house

Finding the length of the shadow of Ajay's house, when the tower cast shadow of 40 m, at the same time:

$\frac{PQ}{XY} = \frac{QR}{YZ}$

Substituting PQ = 100, QR = 40 & XY = 40

$\implies \frac{100}{40} = \frac{40}{YZ}$

$\implies YZ = \frac{40 \times 40}{100}$

$\implies \boxed{\bold{YZ = 16\:m}}$ ← The length of the shadow of Ajay's house

Finding the length of the shadow of Vijay's house, when the tower cast shadow of 40 m, at the same time:

$\frac{AB}{PQ} = \frac{BC}{QR}$

Substituting AB = 20, QR = 40 & PQ = 100

$\implies \frac{20}{100} = \frac{BC}{40}$

$\implies BC = \frac{20 \times 40}{100}$

$\implies \boxed{\bold{BC = 8\:m}}$ ← The length of the shadow of Vijay's house

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Also View:

A vertical row of trees 20 m long casts a shadow 16 m long on the ground. At the same time, a tower casts a shadow 48 m long on the ground.  

(1) Determine the height of the tower  

fit) Which mathematical concept is used in this problem?

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The ratio of the height of a tower and the length of its shadow on the ground is√3:1 what is the angle of elevation of the sun

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Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay's house is 20 m when Vijay's house casts a shadow 10 m long on the ground. At the same time, the tower casts a shadow 50 m long on the ground. At the same time, the house of Ajay casts 20 m shadow on the ground

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