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?

Jun 8, 2018

Let the height of the kangaroo be ${y}_{1} = 5 \text{ ft}$

Let the length of the shadow of the kangaroo be ${x}_{1} = 7 \text{ ft}$

Let the unknown height of the tree be ${y}_{2}$

Let the length of the shadow of the tree be ${x}_{2} = 35 \text{ ft}$

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:

${y}_{2} = \left(5 \text{ ft") (35" ft")/(7" ft}\right)$

${y}_{2} = 25 \text{ ft}$