A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft long. The triangle sjown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft tall, how tall is the tree?
I got 20 ft. I made a proportion 5/2.5=x/10. Is this right?
Yes, that's correct.
Yes, your approach is correct. To solve for the height of the tree, you can set up a proportion between the height of the boy and the length of his shadow, and the height of the tree and the length of its shadow.
Using the proportions, we have:
Boy's height / Boy's shadow = Tree's height / Tree's shadow
Substituting the given values:
5 ft / 2.5 ft = x / 10 ft
Now we can cross multiply:
(5 ft) * (10 ft) = (2.5 ft) * x
50 ft = 2.5 ft * x
To solve for x, we divide both sides of the equation by 2.5 ft:
x = 50 ft / 2.5 ft
Simplifying the right side:
x = 20 ft
Therefore, the height of the tree is 20 ft. So your calculation is correct.
Yes, you are correct! To solve this problem, you can use the concept of similar triangles to set up a proportion and find the height of the tree.
In this case, you correctly set up the proportion:
5/2.5 = x/10
Here, the height of the boy is 5 ft and the length of his shadow is 2.5 ft. The height of the tree is represented by x, and the length of the tree's shadow is 10 ft.
To solve the proportion, you can cross-multiply: 5 * 10 = 2.5 * x
This simplifies to: 50 = 2.5x
To isolate x, divide both sides of the equation by 2.5: x = 50/2.5
Simplifying this gives you: x = 20
Therefore, the height of the tree is 20 ft. Well done!