2.6 Changing the Subject of Formula

2.6 Changing the Subject of Formula

A formula expresses the precise relationship between various measurable quantities in a problem or situation in an equation form.

The figure on the right is of a rectangle. Its length is $\ell$ units and width is $w$ units. Let $P$ be its perimeter.

Now, $P = \ell + w + \ell + w$

$= 2\ell + 2w$

$P = 2(\ell + w)$ units

We have constructed a formula for perimeter ($P$) of a rectangle. In the above formula $P = 2(\ell + w)$, the letter $P$ on the left-hand-side is defined as the subject of the formula, while the letters on the right-hand-side are called terms of the formula.

Perimeter ($P$) of square of length ($\ell$) is $P = 4\ell$.

We change the subject $P$ and rewrite this formula as $\ell = \dfrac{1}{4}P$. $\ell$ has become subject of the formula. If value of $P$ is given, then we can directly find the value of $\ell$.

Example 18

The area of a circle is $A = \pi r^2$. Make $r$ the subject of the formula.

Solution $A = \pi r^2$

or $\pi r^2 = A$

$r^2 = \dfrac{A}{\pi}$

$\therefore r = \sqrt{\dfrac{A}{\pi}}$ [$r$ is always positive]