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?

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?

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.

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.