George has been hired to paint the smith's house. He needs to be sure his ladder will reach the highest part of the house, so he decides to use the shadow method. The measuring stick is 3 ft., and shadow is 5 feet. The shadow of the house is 45 feet. The shadow of the house is 45 feet. The triangles formed are similar. How many feet high is the house?
Cross multiply and solve for x.
3/5 = x/45
27
To find the height of the house, we can set up a proportion using the similar triangles formed by the ladder and the house. We have the following information:
Measuring stick = 3 ft
Shadow of measuring stick = 5 ft
Shadow of the house = 45 ft
Let's set up the proportion using the lengths of the shadows:
(measuring stick shadow) / (measuring stick length) = (house shadow) / (house height)
Plugging in the given values:
(5 ft) / (3 ft) = (45 ft) / (house height)
Now we can solve for the house height by cross-multiplying and isolating the variable:
(5 ft) * (house height) = (3 ft) * (45 ft)
5 * house height = 3 * 45
5 * house height = 135
house height = 135 / 5
house height = 27 ft
Therefore, the house is 27 feet high.