Question

If a school's 50 foot flagpole casts a 75 foot shadow, how long will the shadow be fore a 5 foot tall girl standing near the flagpole at the same time of day?

Answer 1

7.5 feet

Step-by-step explanation:

This is a classic example of a proportional relationship between the height of an object and the length of its shadow.

Given that the flagpole's height is 50 feet and casts a 75-foot shadow, you can set up a proportion to find the length of the shadow for the 5-foot tall girl.

Let's set up the proportion:

Flagpole height : Flagpole shadow = Girl's height : Girl's shadow

This can be represented as:

50 feet : 75 feet = 5 feet : x

To find the length of the girl's shadow (x), you can solve for x using this proportion:

x = (5 feet * 75 feet) / 50 feet

x = 375 / 50

x = 7.5 feet

Therefore, the 5-foot tall girl's shadow would be 7.5 feet long when standing near the flagpole at the same time of day.

Answer 2

To find the length of the shadow for the 5 foot tall girl standing near the flagpole, we can use the concept of similar triangles. By setting up a proportion, we find that the length of the girl's shadow is 7.5 feet.

Step-by-step explanation:

To find the length of the shadow for the 5 foot tall girl standing near the flagpole, we can use the concept of similar triangles.

Let's set up a proportion. The height of the flagpole is 50 feet and the length of its shadow is 75 feet. The height of the girl is 5 feet and we need to find the length of her shadow.

Using the proportion, we have: (50 / 75) = (5 / x), where x is the length of the girl's shadow.

Cross multiplying gives us: 50x = 75 * 5.

Dividing both sides by 50, we get: x = (75 * 5) / 50 = 7.5.

Therefore, the length of the shadow for the 5 foot tall girl will be 7.5 feet.