allison is 5 ft tall. one afternoon her shadow measured 2.5 ft. at the same time, the shadow of her favorite tree was 14.5 feet.
what is the height of the tree
To find the height of the tree, we can use the concept of similar triangles.
Let the height of the tree be x feet.
We have the proportion: (height of Allison) / (shadow of Allison) = (height of the tree) / (shadow of the tree)
Substituting the given values: 5 ft / 2.5 ft = x ft / 14.5 ft
Cross-multiplying, we get: 5 ft * 14.5 ft = 2.5 ft * x ft
Simplifying, we have: 72.5 ft = 2.5 ft * x ft
Dividing both sides by 2.5 ft, we find: x ft = 72.5 ft / 2.5 ft
Therefore, the height of the tree is x = 29 feet.