If a tree 24 m high casts a shadow of 15 m, then the height of a pole that casts a shadow of 6 m under similar conditions is 9.6 m. State whether the statement is true (T) or false (F)
Solution:
The statement made above is true(T).
Height of the Tree Length of the Shadow
24m 15m
Height of the Pole Length of the Shadow
X = ? 6
Under similar conditions the length of shadow of any two objects will be proportional to their height or length. There we can write
Length of the Shadow of an object(L) ∝ Height of the of the object(H). Therefore
Height of the Pole(x) is calculated as:
x = 24 × (6/15)
x = 8 × (6/5)
x = 48/5
x = 9.6 m
✦ Try This: If a tree 27 m high casts a shadow of 18 m, then a pole of height 24 m height will cast a length of 15m?
Height of the Tree Length of the Shadow
27m 18m
Height of the Pole Length of the Shadow
24 m x = ?
Under similar conditions the length of shadow of any two objects will be proportional to their height or length. There we can write
Length of the Shadow of an object(L) ∝ Height of the of the object(H). Therefore
Length of the shadow(x) is calculated as:
x = 18 × (24/27)
x = 18 × (8/9)
x = 2 × 8
x = 16 m
The statement is False because the length of the shadow is 16 m.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13
NCERT Exemplar Class 8 Maths Chapter 10 Problem 49
If a tree 24 m high casts a shadow of 15 m, then the height of a pole that casts a shadow of 6 m under similar conditions is 9.6 m. State whether the statement is true (T) or false (F)
Summary:
“If a tree 24 m high casts a shadow of 15 m, then the height of a pole that casts a shadow of 6 m under similar conditions is 9.6 m.” is a True statement
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