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Raghu is trying to find the height of a tower near his house, using the properties of similar triangles. The height of Raghu's house is $12$ m. When Raghu's house casts a shadow $6$ m long on the ground, the tower casts a shadow $40$ m long on the ground. At the same time, the house of his friend Ramesh casts $12$ m long shadow on the ground.
Based on the above information, answer the following :
(i) What is the height of the tower ?
(ii) What is the height of Ramesh's house ?
(iii) (a) When the tower casts a shadow of $60$ m long, what will be the length of shadow of Ramesh's house ?
OR
(iii) (b) When the tower casts a shadow of $48$ m long, what will be the length of shadow of Raghu's house ?
Based on the above information, answer the following :
(i) What is the height of the tower ?
(ii) What is the height of Ramesh's house ?
(iii) (a) When the tower casts a shadow of $60$ m long, what will be the length of shadow of Ramesh's house ?
OR
(iii) (b) When the tower casts a shadow of $48$ m long, what will be the length of shadow of Raghu's house ?
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Using similarity of triangles:
(i) $\frac{x}{40} = \frac{12}{6} \implies x = 80$ i.e Height of the tower $= 80$ m
(ii) $\frac{12}{6} = \frac{y}{12} \implies y = 24$ i.e. Height of the Ramesh's house $= 24$ m
(iii) (a) $\frac{80}{60} = \frac{24}{a} \implies a = 18$ m i.e length of shadow of Ramesh's house $= 18$ m
OR
(iii) (b) Let $b$ be the length of Raghu's house $\frac{80}{48} = \frac{12}{b} \implies b = 7.2$ m i.e length of shadow of Raghu's house $= 7.2$ m
(i) $\frac{x}{40} = \frac{12}{6} \implies x = 80$ i.e Height of the tower $= 80$ m
(ii) $\frac{12}{6} = \frac{y}{12} \implies y = 24$ i.e. Height of the Ramesh's house $= 24$ m
(iii) (a) $\frac{80}{60} = \frac{24}{a} \implies a = 18$ m i.e length of shadow of Ramesh's house $= 18$ m
OR
(iii) (b) Let $b$ be the length of Raghu's house $\frac{80}{48} = \frac{12}{b} \implies b = 7.2$ m i.e length of shadow of Raghu's house $= 7.2$ m