A child 4 feet tall casts a shadow 6 feet long. A nearby tree casts a shadow 27 feet long. How tall is the tree?
the height is 2/3 as long as the shadow.
so, the height of the tree is 2/3 * 27 = 18 ft
18 ft
To find the height of the tree, we can set up a proportion using the information given. Proportions are used to compare two ratios and find an unknown value.
Let's denote the height of the tree as "h".
The child's height is 4 feet, and the length of the child's shadow is 6 feet.
The tree's shadow is 27 feet.
We can set up the following proportion:
(child's height) / (child's shadow) = (tree's height) / (tree's shadow)
By substituting the given values, we get:
4 feet / 6 feet = h / 27 feet
Now, we can solve for "h" using cross multiplication.
Cross multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio and vice versa:
(4 feet) * (27 feet) = 6 feet * (h)
108 feet = 6h
Now, we can solve the equation for "h" by dividing both sides by 6:
h = 108 feet / 6
h = 18 feet
Therefore, the tree is 18 feet tall.