Chapter 6, Problem 1E

To determine

To calculate:The height of Alexandria when the shadow is $2\frac{1}{5}$ feet long. At the same time, the height of roller coaster is $155$ feet and shadow is $66$ feet long.

Answer to Problem 1E

The height of Alexandria is $62$ inches.

Explanation of Solution

Given information:

Shadow of Alexandria $=2\frac{1}{5}$ feet

Height of Roller Coaster $=155$ feet

Shadow of Roller Coaster $=66$ feet

Formula Used:

$1$ foot $=12$ inches

Calculation:

Let the height of Alexandria be $h$ .

Converting mixed fraction to improper fraction $=2\frac{1}{5}$ $=\frac{11}{5}$ feet

Height to Shadowfractionsare as follows:

Fraction of Roller Coaster $=\frac{155}{66}$

Fraction of Alexandria $=\frac{h}{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}=\frac{5h}{11}$

Since, the height to shadow fractions are for the same time, comparing both the fractions−

  $\frac{155}{66}$ $=\frac{5h}{11}$

Solving the above equation, we have:

  $h=\frac{31}{6}$

Thus, the height of Alexandria is $\frac{31}{6}$ feet.

Since, $1$ foot $=12$ inches

Thus, $\frac{31}{6}$ feet $=62$ inches

The height of Alexandria is $62$ inches.