Question

If the area of a rectangle is 12mn^2 and the width is 3m^2n, what would be the length of the rectangle, given that length is found by dividing area by length?

Answer 1

Let's see

• Area=Length×Breadth

$\\ \rm\rightarrowtail 3m^2n(L)=12mn^2$

$\\ \rm\rightarrowtail mL=4n$

$\\ \rm\rightarrowtail L=4n/m$

Answer 2

Answer:

$\sf length=\dfrac{4n}{m}$

Step-by-step explanation:

Area of a rectangle = width × length

Given:

• $\sf area=12mn^2$
• $\sf width=3m^2n$

Substituting the given expressions into the equation:

$\sf \implies 12mn^2=3m^2n \times length$

$\sf \implies length=\dfrac{12mn^2}{3m^2n}$

Factor 12 to 3 · 4:

$\sf \implies length=\dfrac{3 \cdot 4mn^2}{3m^2n}$

Cancel the common factor of 3:

$\sf \implies length=\dfrac{4mn^2}{m^2n}$

Simplify $\sf \dfrac{n^2}{n}=n$ :

$\sf \implies length=\dfrac{4mn}{m^2}$

Simplify $\sf \dfrac{m}{m^2}=\dfrac{1}{m}$ :

$\sf \implies length=\dfrac{4n}{m}$