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

`\sf length=(4n)/(m)`

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 * length`

`\sf \implies length=(12mn^2)/(3m^2n)`

Factor 12 to 3 · 4:

`\sf \implies length=(3 \cdot 4mn^2)/(3m^2n)`

Cancel the common factor of 3:

`\sf \implies length=(4mn^2)/(m^2n)`

Simplify
`\sf (n^2)/(n)=n` :

`\sf \implies length=(4mn)/(m^2)`

Simplify
`\sf (m)/(m^2)=(1)/(m)` :

`\sf \implies length=(4n)/(m)`