Marcia is 1.5 meters tall. She casts a shadow that is 2 meters long. A nearby building casts a shadow that is 24 meters long. How tall is the building?
(Hint: Use the properties of similar triangles.)
A. 48 m
B. 36 m
C. 18 m
D. 7 m
18
18
To determine the height of the building, we can use the properties of similar triangles. Similar triangles have proportional sides.
First, let's consider the triangle formed by Marcia's height and her shadow. We have a right triangle with a height of 1.5 meters and a shadow length of 2 meters.
Next, let's consider the triangle formed by the building's height and its shadow. We have a right triangle with an unknown height (let's call it h) and a shadow length of 24 meters.
Since the two triangles are similar, we can set up a proportion to find the height of the building:
(Marcia's height) / (Marcia's shadow length) = (Building's height) / (Building's shadow length)
Substituting the values we know, we have:
1.5 / 2 = h / 24
Now, we can solve for h by cross-multiplying:
1.5 * 24 = 2 * h
36 = 2h
Divide both sides by 2:
h = 36 / 2
h = 18
Therefore, the height of the building is 18 meters.
So, the answer is option C: 18 m.
Here's a proportion that solves the problem.
1.5 / 2 = x / 24
2x = 36
x = ?