Question

On sunny day, a 5-foot red kangaroo casts a shadow that is 7 feet long. The shadow of a nearby eucalyptus tree is 35 feet long. How do you write and solve a proportion to find the height of the tree?

Answer 1

Let the height of the kangaroo be `y_1 = 5" ft"`

Let the length of the shadow of the kangaroo be `x_1 = 7" ft"`

Let the unknown height of the tree be `y_2`

Let the length of the shadow of the tree be `x_2 = 35" ft"`

The proportion is:

`y_1/x_1=y_2/x_2`

Solve for `y_2`:

`y_2 = y_1 x_2/x_1`

Substitute in the known values:

`y_2 = (5" ft") (35" ft")/(7" ft")`

`y_2 = 25" ft"`