Paula casts a shadow 2 meters long at the same time a tree casts a shadow 28 meters long. The tree is 17.5 meters tall. How tall is Paula?
1.25
Use a proportion, cross multiply and solve for x.
2/x = 28/17.5
3.2
1.25
Set up a proportion and cross multiply
To find out how tall Paula is, we can use the concept of similar triangles. Similar triangles have corresponding angles that are equal and corresponding sides that are in proportion.
In this case, we can consider the height of the tree as one side of the triangle and its shadow as the corresponding side. Let's assign variables to the unknowns:
- Let "x" represent the height of Paula.
- Let "y" represent the length of Paula's shadow.
We can set up the following proportion:
(x / y) = (17.5 / 28)
Now, we can solve this proportion to find the value of "x," which represents Paula's height.
To do this, we can cross-multiply and then solve for "x":
28x = 17.5y
Divide both sides of the equation by 28:
x = (17.5y) / 28
Given that Paula's shadow is 2 meters long, we can substitute "2" for "y" in the equation:
x = (17.5 * 2) / 28
Now, calculate the expression on the right side of the equation:
x = 35 / 28
Divide 35 by 28:
x = 1.25 meters
Therefore, Paula is 1.25 meters tall.