I need a step by step solution to this problem. I'm preparing for the GKT and I can't remember how to solve these problems. This is just a sample question from the gkt practice packet.
A building 51 feet tall casts a shadow 48 feet long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue?
the ratio of height/shadow is the same for both objects. So,
51/48 = h/16
To solve this problem, you can use the concept of similar triangles.
Step 1: Understand the problem: The problem states that a building casts a shadow that is 48 feet long, and it is 51 feet tall. At the same time, a nearby statue casts a shadow that is 16 feet long. We need to find the height of the statue.
Step 2: Set up a proportion: We can set up a proportion between the heights and the lengths of the shadows. Let's call the height of the statue "x". This means that the proportion would be:
(Height of the building) / (Length of the building's shadow) = (Height of the statue) / (Length of the statue's shadow)
Step 3: Plug in the given values: We can now substitute the given measurements into the proportion.
51 ft / 48 ft = x / 16 ft
Step 4: Solve for x: To solve for x, we need to cross-multiply and then solve for x.
Cross-multiplying gives us:
51 ft * 16 ft = 48 ft * x
Step 5: Simplify the equation: On the left side, we have 816 ft. On the right side, we have 48x.
816 ft = 48x
Step 6: Solve for x: To solve for x, we need to isolate it, so divide both sides of the equation by 48.
816 ft / 48 = x
x ≈ 17 ft
Step 7: Answer the question: The height of the statue is approximately 17 feet.