A tree casts a shadow that measures 5 m. At the same time, a meter stick casts a shadow that is 0.4 m long. How tall is the tree?

Set up a proportion and cross multiply. Let x = height of tree.

x / 5 = 1 / 0.4
0.4x = 5
x = ?

12.5

To find the height of the tree, we can use the concept of similar triangles.

Let's denote the height of the tree as 'h'.

According to the problem, the shadow of the tree is 5 m long, and the shadow of the meter stick is 0.4 m long.

Using the concept of similarity, we can set up the following proportion:

(tree height)/(tree shadow length) = (meter stick height)/(meter stick shadow length)

(h)/5 = 1/0.4

Now, we can solve this proportion to find the height of the tree.

(h)/5 = 1/0.4

Cross-multiplying, we get:

0.4h = 5

Dividing both sides by 0.4:

h = 5 / 0.4

h ≈ 12.5

Therefore, the height of the tree is approximately 12.5 meters.

To find the height of the tree, we can use the concept of similar triangles. Similar triangles have the same shape but can be of different sizes. In this case, we can consider the tree, its shadow, the meter stick, and its shadow as two sets of similar triangles.

Let's assume the height of the tree is "h" meters and the length of its shadow is "s" meters.

Using the given information, we have:
Length of the tree's shadow = 5 meters
Length of the meter stick's shadow = 0.4 meters

Now, we can set up a proportion to solve for the height of the tree:

h / s = meter stick's shadow length / tree's shadow length

Plug in the values:
h / 5 = 0.4 / 0.4

Simplifying the equation:
h / 5 = 1

To solve for h, we can multiply both sides of the equation by 5:
h = 5

Therefore, the height of the tree is 5 meters.