Final answer:
To find the height of the tree outside the room, we apply the principles of similar triangles, using the given size of the image and distances from the window. The height of the tree is calculated to be 0.169m or 16.9cm.
Step-by-step explanation:
The student is asking for help with a problem involving similar triangles and proportions, which is categorically a part of mathematics. The problem describes a scenario where a small hole in a window shutter creates an image of a car on the opposite wall of a room, and we need to use the given dimensions to determine the height of an object (a tree) outside the room.
To solve this, we can use the concept of similar triangles. The ratio of the height of the image to the distance from the shutter to the wall (inside the room) should be equal to the ratio of the height of the tree to the distance from the shutter to the tree (outside the room).
The given values are:
Image height = 6.5m
Room length = 12.5m (distance from shutter to the opposite wall)
Tree distance from window = 32.5cm (which is 0.325m, converting cm to m for consistency in units)
The unknown we are looking to find is the height of the tree.
Using proportions we have:
Height of the tree / Distance of the tree from the window = Height of the image / Distance of the image from the shutter
Solving for the height of the tree:
Height of the tree = Height of the image * (Distance of the tree from the window / Distance of the image from the shutter)
Height of the tree = 6.5m * (0.325m / 12.5m) = 0.169m or 16.9cm.