A tree casts a shadow that measures 5m. At the same time, a meter stick casts a shadow that is o.4m long. How tall is the tree?
The ratios of height to shadow length are the same for both. Thus
X/5 = 1/0.4 = 2.5
Solve for the height X.
To find the height of the tree, we can use the concept of similar triangles. Let's set up the proportion:
(height of the tree) / (length of the tree's shadow) = (height of the meter stick) / (length of the meter stick's shadow)
Let's assign variables for the unknowns:
Let h be the height of the tree.
Let s be the length of the tree's shadow.
Let 1 be the height of the meter stick (which is 1 meter).
Let 0.4 be the length of the meter stick's shadow.
Now we can rewrite the proportion:
h / s = 1 / 0.4
To find the height of the tree, we can solve this proportion by cross-multiplying:
h * 0.4 = s * 1
0.4h = s
Finally, we can substitute the given values into the equation and solve for the height of the tree.
0.4h = 5
Divide both sides of the equation by 0.4:
h = 5 / 0.4
Simplify the right side:
h = 12.5
Therefore, the height of the tree is 12.5 meters.