A tree cast a 24 foot shadow at the same time a fence post 5 feet high cast a 4 foot shadow. How tall is the tree?
Cross multiply and solve for x.
5/4 = x/24
5/4*x/24 4x=120 divide through by the coefficient of x,which is 4.120/4=30 therefore x=30
To find the height of the tree, we can use the concept of similar triangles.
Let's assume the height of the tree is represented by 'x'.
According to the given information, the tree casts a 24-foot shadow, and the fence post casts a 4-foot shadow.
We have two similar triangles, where the corresponding sides are proportional.
The height of the tree (x) corresponds to the height of the fence post (5 feet), and the length of the shadow of the tree (24 feet) corresponds to the length of the shadow of the fence post (4 feet).
Using the proportion:
x/5 = 24/4
Cross multiplying, we get:
4x = 5 * 24
Simplifying the equation:
4x = 120
Dividing both sides by 4:
x = 120/4
x = 30
Therefore, the height of the tree is 30 feet.
To determine the height of the tree, we can set up a proportion using the concept of similar triangles.
Let's assume the height of the tree is represented by 'x'. We can set up the following proportion:
(height of tree)/(length of its shadow) = (height of fence post)/(length of its shadow)
In this case, the height of the fence post is given as 5 feet and the length of its shadow is given as 4 feet. We need to find the height of the tree, which is represented as 'x', and the length of its shadow is 24 feet.
Using the proportion, we have:
x/24 = 5/4
To solve for 'x', we can cross-multiply and then solve for 'x':
4x = 24 * 5
4x = 120
x = 120/4
x = 30
Therefore, the height of the tree is 30 feet.