Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 3

3 / 5

Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm.

Find the linear pattern representing the area of the rectangle.

Answer

1
Use the area formula for a rectangle and substitute each given breadth.
\text{Area = length × breadth = ${color:#2E2EFF}13{/color}$ × breadth}
\text{(i) $13 × {color:#2E2EFF}12{/color} = 156 cm^2$ $\quad$ ${color:#625b5f}[breadth = 12 cm]{/color}$}
\text{(ii) $13 × {color:#2E2EFF}10{/color} = 130 cm^2$ $\quad$ ${color:#625b5f}[breadth = 10 cm]{/color}$}
\text{(iii) $13 × {color:#2E2EFF}8{/color} = 104 cm^2$ $\quad$ ${color:#625b5f}[breadth = 8 cm]{/color}$}
2
Write the areas in the given order.
Answer: The areas are 156 cm^2, 130 cm^2, and 104 cm^2.
3
Compare consecutive areas to find the common difference.
\text{130 - 156 = -26 cm^2 $\quad$ ${color:#625b5f}[breadth changes from 12 cm to 10 cm]{/color}$}
\text{104 - 130 = -26 cm^2 $\quad$ ${color:#625b5f}[breadth changes from 10 cm to 8 cm]{/color}$}
Therefore, the common difference is −26 cm^2.
4
Write the linear pattern for the area.
Answer: The linear pattern is 156, 130, 104, …, with a common difference of −26 cm^2.
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