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If a tree casts a 18 feet shadow and at the same time, a child of height 3 feet casts a 2 feet shadow, then the height of the tree is
  • a)
    27 feet
  • b)
    32 feet
  • c)
    45 feet
  • d)
    36 feet
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a tree casts a 18 feet shadow and at the same time, a child of heig...
Let AB be the height of tree which casts a shadow AC = 18 feet and ED be the height of child which casts a shadow CD = 2 feet.
Now, in ΔABC and ΔDEC, we have 
∠A = ∠D [Each 90°]
∠C = ∠C [Common angle]
∴ ΔABC ~ ΔDEC [By AA similarity]

⇒ AB = 27 feet
So, the height of tree is 27 feet.
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Community Answer
If a tree casts a 18 feet shadow and at the same time, a child of heig...
Given information:
- Height of the child = 3 feet
- Length of the shadow cast by the child = 2 feet
- Length of the shadow cast by the tree = 18 feet

To find: Height of the tree

The height of the tree can be determined by using the concept of similar triangles. The triangles formed by the child, its shadow, the tree, and its shadow are similar.

Similar triangles have proportional sides, meaning their corresponding sides are in the same ratio.

Using this concept, we can set up a proportion to find the height of the tree.

Let's denote:
- Height of the tree = x feet

Proportion:
(height of the tree) / (length of its shadow) = (height of the child) / (length of its shadow)

x / 18 = 3 / 2

Now, we can cross-multiply and solve for x:

2x = 18 * 3

2x = 54

x = 54 / 2

x = 27

Therefore, the height of the tree is 27 feet.

So, the correct answer is option A) 27 feet.
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If a tree casts a 18 feet shadow and at the same time, a child of height 3 feet casts a 2 feet shadow, then the height of the tree isa)27 feetb)32 feetc)45 feetd)36 feetCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a tree casts a 18 feet shadow and at the same time, a child of height 3 feet casts a 2 feet shadow, then the height of the tree isa)27 feetb)32 feetc)45 feetd)36 feetCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a tree casts a 18 feet shadow and at the same time, a child of height 3 feet casts a 2 feet shadow, then the height of the tree isa)27 feetb)32 feetc)45 feetd)36 feetCorrect answer is option 'A'. Can you explain this answer?.
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