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?

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Answer 1 · 2018-06-08T20:34:46

Let the height of the kangaroo be $y_{1} = 5 ft$ $y_1 = 5" ft"$

Let the length of the shadow of the kangaroo be $x_{1} = 7 ft$ $x_1 = 7" ft"$

Let the unknown height of the tree be $y_{2}$ $y_2$

Let the length of the shadow of the tree be $x_{2} = 35 ft$ $x_2 = 35" ft"$

The proportion is:

$\frac{y_{1}}{x_{1}} = \frac{y_{2}}{x_{2}}$ $y_1/x_1=y_2/x_2$

Solve for $y_{2}$ $y_2$ :

$y_{2} = y_{1} \frac{x_{2}}{x_{1}}$ $y_2 = y_1 x_2/x_1$

Substitute in the known values:

$y_{2} = (5 ft) \frac{35 ft}{7 ft}$ $y_2 = (5" ft") (35" ft")/(7" ft")$

$y_{2} = 25 ft$ $y_2 = 25" ft"$