Chapter 6.9, Problem 4PPS

To determine

In calculate: The length of the school building`s shadow using the given information.

Answer to Problem 4PPS

Length of school building`s shadow is 37.5 feet at the same time.

Explanation of Solution

Given information: A height of school building is 25 feet and a mail box is 4 feet high. The mailbox casts a shadow that is 6 feet.

Concept used: The related figure forming two similar triangles can be drawn as:

  

And as in similar triangles, the ratio of corresponding sides are proportional, so

  $\frac{\text{Height of the building}}{\text{Height of mailbox}}=\frac{\text{Length of shadow of building}}{\text{Length of shadow of mailbox}}$

Calculation:

Based on above proportion, set,

  $\frac{AB}{DE}=\frac{BC}{CE}$

Or,

  $\frac{25}{4}=\frac{BC}{6}$

Or, length of shadow of building,

  $\begin{array}{c}BC=\frac{25\times 6}{4}\\ =\frac{150}{4}\\ =37.5\end{array}$ (On cross multiply)

So, the length of shadow of school building is 37.5 feet.