Question

a 12 foot tall building casts on 8 foot long long shadow. how long of a shadow will a 5 foot tall women have

Answer 1

Using the concept of similar triangles and the given ratio of a building's height to its shadow, it was calculated that a 5-foot tall woman would cast a shadow that is approximately 3.33 feet long.

Step-by-step explanation:

The question deals with similar triangles where the ratio of the height of an object to the length of its shadow is constant if the sun's rays are considered to be parallel. Given that a 12-foot tall building casts an 8-foot long shadow, we can use this ratio to determine the length of the shadow that a 5-foot tall woman will cast.

First, find the ratio of the building's height to its shadow's length:

• Height of the building / Length of shadow = 12 feet / 8 feet = 1.5

Since the ratio should remain the same, we can set up a proportion for the woman:

• Height of the woman / Length of her shadow = 5 feet / x (the unknown length of the shadow)

Now solve for 'x' using cross multiplication:

• 12 / 8 = 5 / x
• 12*x = 5*8
• x = (5*8) / 12
• x = 40 / 12
• x = 3.33 feet (approximately)

Therefore, the shadow cast by the 5-foot tall woman will be approximately 3.33 feet long.

Answer 2

This is just a basic proportion. 5/8 = x/12. So the 5 foot tall women would have a 7.5 foot shadow.