Question

3. 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 if 20m when Vijay’s house casts a shadow 10m long on the ground. At the

same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the

ground

i. What is the height of the tower?

a) 20m b) 50m c) 100m d) 200m

ii. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?

a) 75m b) 50m c) 45m d) 60m

iii. What is the height of Ajay’s house?

a) 30m b) 40m c) 50m d) 20m​​

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 if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground

i. What is the height of the tower?

a) 20m b) 50m c) 100m d) 200m

ii. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?

a) 75m b) 50m c) 45m d) 60m

iii. What is the height of Ajay’s house?

a) 30m b) 40m c) 50m d) 20m​​

To find:

i. What is the height of the tower?

ii. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?

iii. What is the height of Ajay’s house?

Solution:

i. Finding the height of the tower:

Let's say,

"AB" → the height of Vijay's house = 20 m

"BC" → the length of the shadow of Vijay's house = 10 m

"PQ" → the height of the tower

"QR" → the length of the shadow of the tower = 50 m

Consider ΔABC and ΔPQR, we have

∠ABC = ∠PQR = 90° . . . [both Vijay's house and the tower are vertical to the ground]

∠ACB = ∠PRQ . . . [since the shadows are cast at the same time ∴ the angle of elevation of the sun is the same in both cases]

∴ Δ ABC ~ Δ PQR . . .  [By AA similarity]

We know that,

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

∴ $\frac{AB }{PQ} = \frac{BC}{QR}$

on substituting the values of AB, BC & QR, we get

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

$\implies \bold{PQ = 100 \:m}$ ← option (c)

Thus, $\boxed{\bold{Height\:of\:the\:tower\:is\:\underline{100\:m}.}}$

ii. Finding the length of the shadow of the tower when Vijay’s house casts a shadow of 12 m:

here we have,

The length of the shadow of Vijay's house, BC = 12 m

The height of the tower, PQ = 100 m

The height of Vijay's house, AB = 20 m

∴ $\frac{AB }{PQ} = \frac{BC}{QR}$

on substituting the values of AB = 20 m, BC = 12 m & PQ = 100 m, we get

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

$\implies \bold{QR = 60 \:m}$ ← option (d)

Thus, $\boxed{\bold{Length\:of\:the\:shadow\:of\:the \:tower\:is\:\underline{60\:m}.}}$

iii. Finding the height of Ajay’s house:

Let's say,

Δ ABC and Δ DEF are the two similar triangles here

"DE" → the height of Ajay's house

"EF" → length of the shadow of Ajay's house = 20 m

∴ $\frac{AB }{DE} = \frac{BC}{EF}$

on substituting the values of AB = 20 m, BC = 10 m & EF = 20 m, we get

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

$\implies \bold{DE = 40 \:m}$ ← option (b)

Thus, $\boxed{\bold{Height\:of\:Ajay's\:house\:is\:\underline{40\:m}.}}$

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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?​

brainly.in/question/14367276

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?

brainly.in/question/2267489

Answer 2

Answer:

Ferns, horsetails (often treated as ferns), and lycophytes (clubmosses, spikemosses, and quillworts) are all pteridophytes. ... "Pteridophyta" is thus no longer a widely accepted taxon, but the term pteridophyte remains in common parlance, as do pteridology and pteridologist as a science and its practitioner, respectively.

Step-by-step explanation:

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