a 6 foot red casts a shadow that is 7 feet long. the shadow of a nearby tree is 42 feet long. slove a proportion to find the height of the tree

the height:shadow ratio is the same, so

x/42 = 6/7

To solve this proportion and find the height of the tree, we can set up the following equation:

(Height of the 6-foot red object) / (Length of its shadow) = (Height of the tree) / (Length of the tree's shadow)

Let's fill in the values we know:

(6 feet) / (7 feet) = (Height of the tree) / (42 feet)

Now, we need to solve for the height of the tree. To do this, we can use cross multiplication:

(6 feet) * (42 feet) = (7 feet) * (Height of the tree)

Now, multiply the numbers on both sides of the equation:

252 feet = 7 feet * (Height of the tree)

Finally, isolate the variable by dividing both sides by 7 feet:

(252 feet) / (7 feet) = Height of the tree

The feet unit cancels out, leaving us with:

36 feet = Height of the tree

Therefore, the height of the tree is 36 feet.