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?


  1. Answer:
    Step-by-step 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.


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