# 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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