roger is 5 feet tall and casts a shadow 3.5 feet longer. at the same time,the flagpole outside his school casts a shadow 14 feet long. write and solve a
Solve this proportion for x.
5/3.5 = x/14
To solve this problem, we need to use the concept of similar triangles. Similar triangles have proportional sides.
Let's set up a proportion to find the height of the flagpole.
The proportion we can set up is:
(height of Roger) / (length of Roger's shadow) = (height of flagpole) / (length of flagpole's shadow)
Plugging in the given values, we have:
5 / (5 + 3.5) = (height of flagpole) / 14
Now, let's solve for the height of the flagpole.
First, simplify the left side of the equation:
5 / 8.5 = (height of flagpole) / 14
Then, cross multiply:
5 * 14 = 8.5 * (height of flagpole)
70 = 8.5 * (height of flagpole)
Now, divide both sides by 8.5 to isolate the height of the flagpole:
height of flagpole = 70 / 8.5
height of flagpole ≈ 8.24 feet