Suppose the length of a rectangle is . Find the area if the breadth is (i) , (ii) , (iii) . Find the linear pattern representing the area of the rectangle.

Understand the Question The area of a rectangle is given by the formula . The length of the rectangle is constant at . For each given breadth, calculate the area by multiplying by the breadth. To find the linear pattern representing the area, express the breadth as a variable , resulting in a linear relation . Part (i) Find the area if the breadth is . Step 1 · Calculate Area for Breadth = 12 cm Given and : Answer > (i) Part (ii) Find the area if the breadth is . Step 1 · Calculate Area for Breadth = 10 cm Given and : Answer > (ii) Part (iii) Find the area if the breadth is . Step 1 · Calculate Area for Breadth = 8 cm Given and : Answer > (iii) Part Find the linear pattern representing the area of the rectangle. Step 1 · Find the Linear Pattern Let the breadth of the rectangle be . With a fixed length of , the area is: Answer > Common Mistakes Unit Errors: Forgetting to write units in square centimeters () for area. Formula Confusion: Using the perimeter formula instead of the area formula .

Introduction to Linear Polynomials | Exercise 2.3

Question 3

Suppose the length of a rectangle is $13\text{ cm}$ . Find the area if the breadth is (i) $12\text{ cm}$ , (ii) $10\text{ cm}$ , (iii) $8\text{ cm}$ . Find the linear pattern representing the area of the rectangle.

Solution

Understand the Question

The area of a rectangle is given by the formula $\text{Area} = \text{Length} \times \text{Breadth}$ .
The length of the rectangle is constant at $13\text{ cm}$ .
For each given breadth, calculate the area by multiplying $13$ by the breadth.
To find the linear pattern representing the area, express the breadth as a variable $x\text{ cm}$ , resulting in a linear relation $A(x) = 13x$ .

(i) Find the area if the breadth is $12\text{ cm}$ .

Step 1 · Calculate Area for Breadth = 12 cm

Given $\text{Length} = 13\text{ cm}$ and $\text{Breadth} = 12\text{ cm}$ :

\begin{aligned} \text{Area} &= \text{Length} \times \text{Breadth} \\[0.6em] &= 13 \times 12 \\[0.6em] &= 156\text{ cm}^2 \end{aligned}

Answer

(i) $156\text{ cm}^2$

(ii) Find the area if the breadth is $10\text{ cm}$ .

Step 1 · Calculate Area for Breadth = 10 cm

Given $\text{Length} = 13\text{ cm}$ and $\text{Breadth} = 10\text{ cm}$ :

\begin{aligned} \text{Area} &= \text{Length} \times \text{Breadth} \\[0.6em] &= 13 \times 10 \\[0.6em] &= 130\text{ cm}^2 \end{aligned}

Answer

(ii) $130\text{ cm}^2$

(iii) Find the area if the breadth is $8\text{ cm}$ .

Step 1 · Calculate Area for Breadth = 8 cm

Given $\text{Length} = 13\text{ cm}$ and $\text{Breadth} = 8\text{ cm}$ :

\begin{aligned} \text{Area} &= \text{Length} \times \text{Breadth} \\[0.6em] &= 13 \times 8 \\[0.6em] &= 104\text{ cm}^2 \end{aligned}

Answer

(iii) $104\text{ cm}^2$

Find the linear pattern representing the area of the rectangle.

Step 1 · Find the Linear Pattern

Let the breadth of the rectangle be $x\text{ cm}$ . Diagram 1

With a fixed length of $13\text{ cm}$ , the area $A$ is:

\begin{aligned} A &= 13 \times x \\[0.6em] &= 13x \end{aligned}

Answer

$A = 13x$

Common Mistakes

Unit Errors: Forgetting to write units in square centimeters ( $\text{cm}^2$ ) for area.
Formula Confusion: Using the perimeter formula $2(\text{length} + \text{breadth})$ instead of the area formula $\text{length} \times \text{breadth}$ .

Question 3

More questions in Exercise 2.3