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**A 23 m 75 cm high water tank casts a shadow 20 m long. Find at the same time;**

**(i) the length of the shadow cast by a tree 9 m 50 cm high.**

**(ii) the height of the tree if the length of the shadow is 12 m.**

Answer:

Given:

Height of a water tank = 23 m 75 cm

= 23 ¾ m = 95/4 m.

Its shadow = 20 m

(i) If height of a tree = 9 m 50 cm

= 9 ½ m

= 19/2 m

Now, let its shadow be ‘x’ m

So, 95/4 : 19/2 :: 20: x

(95/4) × (2/19) = 20/x

5/2 = 20/x

x = (2 × 20)/5

= 8 m

∴ Its shadow = 8 m

(ii) Let the height of a tree be ‘x’ m

and its shadow = 12 m

95/4 : x :: 20: 12

95/4x = 20/12

4x = (95 × 12)/20

x = 57/4 m

x =14 m 25 cm

∴ Height of the tree is14 m 25 cm.

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