# Ex.9.2 Q2 Algebraic Expressions and Identities - NCERT Maths Class 8

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## Question

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.

(i) $$(p,\,q)$$

(ii) $$\left( 10m,\,5n \right)$$

(iii) $$\left( 20 x^2,\,5 y^2 \right)$$

(iv) $$\left( 4x,\,3x^2 \right)$$

(v) $$\left( 3mn,\,4np \right)$$

## Text Solution

What is known?

What is unknown?

Areas of rectangles

Reasoning:

\begin{align} &{\text{Area of a Rectangle}} \\&= \text{Length}\,\times\, \text{Breadth}\end{align}

Steps:

We know that,

\begin{align} &{\text{Area of a Rectangle}} \\&= \text{Length}\,\times\, \text{Breadth}\end{align}

(i) Area of $$1^{\rm st}$$ rectangle

\begin{align} &=p\,\times\,q\\ &= pq\end{align}

(ii) Area of $$2^{\rm nd}$$ rectangle

\begin{align}& = 10m \times5n\\&= 10\times5\times m \times n\\& = 50\,mn \end{align}

(iii) Area of $$3^{\rm rd}$$ rectangle

\begin{align} &= 20{x^2} \times 5{y^2}\\&= {\rm{ }}20{\rm{ }} \times 5\times {x^2} \times {y^2} \\&= 100{x^2}{y^2} \end{align}

(iv) Area of $$4^{\rm th}$$  rectangle

\begin{align} & =4x \times 3{x^2}\\&= 4 \times3 \times x \times {x^2} \\&= 12{x^3} \end{align}

(v) Area of $$5^{\rm th}$$ rectangle

\begin{align} &= 3mn\times 4np\\ &= 3 \times 4 \times m \times n \times n \times p \\&= 12m{n^2}p\end{align}

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