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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?

2 Answers

9 votes

Let's see

  • Area=Length×Breadth


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


\\ \rm\rightarrowtail mL=4n


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

User Ordag
by
8.2k points
13 votes

Answer:


\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)

User Danyhow
by
9.1k points

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