Chapter 12, Problem 13CT

To determine

To calculate: The $h$ when $b=\text{}36$ and $v=108$ ,where $v$ varies jointly as $b$ and $h$ and $v=50$ when $b=\text{}25$ and $h=6$

Answer to Problem 13CT

The value of $h$ is 9 when $b=\text{}36$ and $v=108$ .

Explanation of Solution

Given information:

The variable $v$ varies jointly as $b$ and $h$ and $v=50$ when $b=\text{}25$ and $h=6$ .

Formula used:

If a variable varies directly as the product of two or more variables, then resultant is known as joint variation.

The joint variation expresses as,

  $z\text{}=kxy$ , where $k$ is a nonzero constant.

Calculation:

The variable $v$ varies jointly as $b$ and $h$ as,

  $v=kbh$

Put the values of $v=50$ when $b=\text{}25$ and $h=6$ in equation,

  $\begin{array}{l}v=kbh\\ 50=k\cdot 25\cdot 6\\ \frac{50}{150}=k\\ k=\frac{1}{3}\end{array}$

Put the value of $k=\frac{1}{3}$ in join variation expression,

  $v=\frac{1}{3}bh$

Now, put the values $b=\text{}36$ and $v=108$ in $v=\frac{1}{3}bh$ for value of $h$ ,

  $\begin{array}{l}108=\frac{1}{3}\cdot 36\cdot h\\ 108\cdot 3=36\cdot h\\ \frac{108\cdot 3}{36}=h\\ h=9\end{array}$

Thus, value of $h$ is 9 when $b=\text{}36$ and $v=108$ .