Question

if the area of a rectangle is 16s²t and the length is 8st², what would be the width of the rectangle, given that width is found by dividing area by length? simplify the answer.

$\frac{2}{st}$

$\frac{t}{2s}$

$2st$

$\frac{2s}{t}$

Explanation:

Step1: Set up the division formula

The formula for the width $w$ of a rectangle is $w=\frac{A}{l}$, where $A$ is the area and $l$ is the length. Given $A = 16s^{2}t$ and $l=8st^{2}$, we have $w=\frac{16s^{2}t}{8st^{2}}$.

Step2: Simplify the coefficient

Divide the numerical coefficients: $\frac{16}{8}=2$.

Step3: Simplify the variables using exponent - rules

For the variable $s$, using the rule $\frac{s^{m}}{s^{n}}=s^{m - n}$, we have $\frac{s^{2}}{s}=s^{2-1}=s$. For the variable $t$, $\frac{t}{t^{2}}=t^{1 - 2}=t^{-1}=\frac{1}{t}$.

Step4: Combine the simplified parts

Multiply the simplified coefficient and variables: $2\times s\times\frac{1}{t}=\frac{2s}{t}$.

Answer:

$\frac{2s}{t}$