Question

a 15 m 60 cm high vertical pole casts a shadow 10m 20 cm long find at the same time i) length of the shadow of a house whose height is 20 m 40 cm ii) height of the tree whose shadow is 550 cm​

Answer 1

Given :

• Height of the vertical pole = 15m 60cm
• length of the shadow = 10m 20cm

To Find :

(i) Length of the shadow of a house whose height is 20m 40cm

(ii) height of the house whose shadow is 550cm

Explanation :

• The height and shadow of the object can be founded by using ratios of the similiar height and shadow objects

$\sf\dfrac{height_{(pole)}}{shadow_{(pole)}}=\dfrac{height_{(house)}}{shadow_{(house)}}$

Solution :

• Convert all the measurements to centimetres.

(i) Length of the shadow of a house whose height is 20m 40cm

$\implies \sf\dfrac{height_{(pole)}}{shadow_{(pole)}}=\dfrac{height_{(house)}}{shadow_{(house)}}$

$\implies \sf\dfrac{1560}{1020}=\dfrac{2040}{x}$

$\implies \sf\dfrac{1560}{1020\times 2040}=\dfrac{1}{x}$

$\implies \sf\dfrac{1560}{2080800}=\dfrac{1}{x}$

$\implies \sf \dfrac{2080800}{1560}=x$

$\implies \sf 1333.8cm=x$

(ii) height of the house whose shadow is 550cm

$\implies \sf\dfrac{height_{(pole)}}{shadow_{(pole)}}=\dfrac{height_{(house)}}{shadow_{(house)}}$

$\implies \sf\dfrac{1560}{1020}=\dfrac{y}{550}$

$\implies \sf\dfrac{1560 \times 550}{1020}=y$

$\implies \sf\dfrac{858000}{1020}=y$

$\implies \sf 841.17 cm =y$

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Required Answer :

• Length of the shadow of a house is $\underline{\sf 1333.8 cm}$
• Height of the tree is $\underline{\sf 841.17 cm}$

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