Chapter 6, Problem 47SGR

To determine

To calculate:Tofind how tall is the world’s shortest woman.

Answer to Problem 47SGR

Height of shortest woman is $2$ feet $7$ inches

Explanation of Solution

Given information: At $7$ feet $8$ inches, the world’s tallest woman casts a $46$ inch shadow. At the same time, the world’s shortest woman casts a $15.5$ inch shadow

Calculation:

Given that at $7$ feet $8$ inches, the world’s tallest woman casts a $46$ inch shadow. At the same time, the world’s shortest woman casts a $15.5$ inch shadow

Let the height of shortest woman be $x$

Since the shadow is casted at the same time, hence they must be proportional

Thus, proportional is

  $\frac{x}{15.5}=\frac{92}{46}$

On solving the above proportion,

  $\begin{array}{l}x\times 46=92\times 15.5\\ x=\frac{92\times 15.5}{46}\\ x=\frac{2\times 15.5}{1}\\ x=31\end{array}$

Hence, Height of shortest woman is $31$ inches, which is $2$ feet $7$ inches