A fence post 3ft tall casts a shadow 16ft long . At the same time ,the barn casts
a shadow 96ft long. how tall is the barn?
3/16=x/96
96(3)=16x
288=16x
288/16=16x/16
x=18
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To find the height of the barn, we can use similar triangles.
First, let's define some variables:
- Let h be the height of the barn.
- Let x be the length of the barn's shadow.
- Let 3 be the height of the fence post.
- Let 16 be the length of the fence post's shadow.
We can set up a proportion between the similar triangles:
Height of barn / Length of barn's shadow = Height of fence post / Length of fence post's shadow
h / x = 3 / 16
Now, we can solve for h by cross-multiplying:
h * 16 = 3 * x
Divide both sides of the equation by 16:
h = (3 * x) / 16
Given that the length of the barn's shadow is 96 ft, we can substitute x = 96:
h = (3 * 96) / 16
Simplifying the equation:
h = 288 / 16
h = 18
Therefore, the height of the barn is 18 feet.