Standing by a pole, a boy 3(1/2)feet tall casts a 6-foot shadow. The pole casts a 24-foot shadow. How tall is the pole?
14 feet.
18 feet.
28 feet.
41 feet.
Detailed Explanation
Let's denote the height of the pole as "h" in feet.
According to the problem, the boy's height is 3(1/2) feet, which can be written as 3.5 feet. The length of the boy's shadow is 6 feet.
Similarly, the length of the pole's shadow is 24 feet.
We can set up the following proportion:
(Height of the boy) / (Length of the boy's shadow) = (Height of the pole) / (Length of the pole's shadow)
Plugging in the values, we have:
3.5 feet / 6 feet = h / 24 feet
To solve for "h," we can cross-multiply and then divide:
6 feet * h = 3.5 feet * 24 feet
6h = 84
Dividing both sides by 6:
h = 84 / 6
h = 14
Therefore, the height of the pole is 14 feet.
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