Question

A cactus casts a shadow that is 15 ft long. A gate nearby casts a shadow that is 5 ft long at the same moment. If the height of a gate is 3ft long, what is the height of the cactus?

Answer 1

Explanation:

There is more than 1 way to do this problem, but all of them involve proportions. It's a good idea to learn how a proportion works: it's one of the key tools of the sciences.

Let the height of the Cactus = x

Ratio Cactus = Ratio Gate.

x/15 = 3/5

Notice that both ratios are set up as height / shadow. If you do this all the time (keep the ratio the same), you will never make a mistake on proportions.

x/15 = 3/5 Cross Multiply

5x = 15 * 3 Combine.

5x = 45 Divide by 5

5x/5 = 45/5

x = 9

The height of the cactus has to be less than the length of its shadow, which it is.