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: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 = xRatio Cactus = Ratio Gate.x/15 = 3/5Notice 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 Multiply5x = 15 * 3 Combine.5x = 45 Divide by 55x/5 = 45/5x = 9The height of the cactus has to be less than the length of its shadow, which it is.