A 12 foot-high pole casts a 9 foot long shadow, at the same time of day, what would be the length of a shadow cast by a 45 foot-long tree

To find the length of the shadow cast by a 45-foot-long tree, we can use a proportion.

Let's set up a proportion using the given information:

Proportion: height of the pole / length of the pole's shadow = height of the tree / length of the tree's shadow

From the given information, we have:
height of the pole = 12 feet
length of the pole's shadow = 9 feet

Let's substitute these values into the proportion:

12 feet / 9 feet = height of the tree / length of the tree's shadow

Now we need to solve for the unknown length of the tree's shadow.

Cross-multiplying the proportion:

12 feet * length of the tree's shadow = 9 feet * height of the tree

We can simplify this:

12 * length of the tree's shadow = 9 * height of the tree

Now, since we want to find the length of the tree's shadow, we rearrange the equation:

length of the tree's shadow = (9 * height of the tree) / 12

Next, we substitute the height of the tree:

length of the tree's shadow = (9 * 45 feet) / 12

Calculating this:

length of the tree's shadow = (405 feet) / 12

Simplifying:

length of the tree's shadow = 33.75 feet

Therefore, the length of the shadow cast by the 45-foot-long tree would be approximately 33.75 feet.

13

Use a proportion.

12/9 = 45/x

Cross multiply and solve for x.