Re: The figure represents a boy who is 1.6 m tall standing in front of a l
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07 Jan 2021, 14:38
Given, The figure represents a boy who is 1.6 m tall standing in front of a lamppost that is 8 m tall. As shown, the boy casts a shadow that is 1.5 m long when he is 6 m from the lamppost.
Note that 8/1.6=(6+1.5)/1.5. As the boy walks in a straight line away from the lamppost, his distance from the lamppost increases and his shadow gets longer. It is important to note down.
When the boy is 7 m from the lamppost, he casts a shadow that is 1.75 m long. (It is another example given)
If we look closely, height of lamp post / height of the boy
= (Distance of boy from Lamp post + length of his shadow ) /length of his shadow; it is from the property of similar triangles.
When the boy is 8 m from the lamppost, he casts a shadow that is__________m long.
So, we got, height of lamp post / height of the boy
= (Distance of boy from Lamp post + length of his shadow)/length of his shadow
or, 8/1.6 = (8+x)/x; say x= length of his shadow
or, 5x= 8+x or x= 8/4 = 2 m. Ans. A.
When the boy casts a shadow that is 3 m long, he is__________m from the lamppost.
So, we got, height of lamp post / height of the boy
= (Distance of boy from Lamp post + length of his shadow)/length of his shadow
or, 8/1.6 = (y+3)/3; say y= Distance of boy from Lamp post
or, 15= y+3 or y= 12 m. Ans. A.