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

## 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?**

Lengths and breadths of rectangles

**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

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