how high is a tree that cast a 24-foot shadow at the same time a 9-foot pole casts a shadow which is 3-feet long

Cross multiply and solve for x.

9/3 = x/24

40?

To find the height of the tree, we can use similar triangles.

Let's define:
h = height of the tree
s = length of the shadow cast by the tree
p = height of the pole
q = length of the shadow cast by the pole

According to the given information:
s = 24 feet (length of the shadow cast by the tree)
p = 9 feet (height of the pole)
q = 3 feet (length of the shadow cast by the pole)

We can set up the following proportion between the similar triangles:

h / s = p / q

Plugging in the known values:
h / 24 = 9 / 3

Simplifying the equation:
h / 24 = 3

Cross-multiplying:
h = 24 * 3

Calculating:
h = 72 feet

Therefore, the height of the tree is 72 feet.

To determine the height of the tree, we can use the concept of similar triangles. When two objects cast shadows at the same time, the lengths of their shadows are proportional to their heights.

Let's denote the height of the tree as "h" and the length of its shadow as "s". Similarly, we denote the height of the pole as "p" and the length of its shadow as "x".

We can set up a proportion based on the given information:

(s / x) = (h / p)

Plugging in the given values:
(24 / 3) = (h / 9)

Now, we can solve for "h" by cross-multiplying and then dividing:

24 * 9 = 3 * h
216 = 3h
h = 216 / 3
h = 72

Therefore, the height of the tree is 72 feet.