Question

Explain how to solve the word problem over similar figures.

John is 5 feet tall and casts a shadow that is 12 feet tall. The building he is standing next to is 25 feet tall. How many feet would the shadow of the building be?

Answer 1

The building's shadow will be 60 feet.

Explanation:

Think of John as a vertical line, and his shadow as a horizontal line on a 90 degree angle, and well as the building and it's shadow.

This is a proportions problem, so you want to match the similar items, right? John and the building are similar, and the two shadows are similar.

Now, set up fractions so you can butterfly multiply to get x, the shadow of the building. John/JohnShadow = Building/BuildingShadow. These two will equal the same thing because they are the same proportion.

5/12 = 25/x

5(x) = 12(25)

5x = 300

x = 300/5

x = 60

The building's shadow will be 60 feet. If you do the math, 5/12 = .4167, and 25/60 = .4167, so the proportions match. Hope this helps, comment if you are confused!