Page 132 - ICSE Math 6

(b) The rule for pattern of letter A is given in the following table.

…
Number of letters ‘A’ 1 2 3 4 5 … n
Number of matchsticks 6 10 14 18 22 … 4n + 2

Example 2: If there are 60 apples in a box, how will you write the total
number of apples in terms of the number of boxes?
Solution: Number of apples in each box = 60
Let the number of boxes be n.
Therefore, total number of apples = 60 × n = 60n
Example 3: Sita is 7 years younger to Radha. Write Radha’s age in terms of Sita’s age.
Solution: Let Sita’s age be x years.
Since Sita is 7 years younger, therefore Radha is 7 years older.
Hence, Radha’s age = (x + 7) years

Use of Variables
Let’s learn how variables can be used to denote characteristics of certain geometric figures.
(a) Perimeter of a square
Perimeter = 4 times the length of a side of the square
= 4 × l = 4l
Thus, perimeter of a square having side l is 4l. l
(b) Area of a rectangle
Area = length of the rectangle × breadth of the rectangle
Thus, area of a rectangle having length and breadth l and b respectively is l × b. b
Here, l and b are variables. They can take any value independent of each other. l

Example 4: A cube is a three-dimensional figure as shown in the figure.
It has six faces and all of them are identical squares. The
length of an edge of the cube is given by l. Find the formula
for the total length of the edges of a cube. l
Solution: The length of an edge of the cube = l l

Number of edges in a cube = 12 l
Therefore, the total length of the edges of the given cube is 12l.

EXERCISE 11.1

1. Separate the constants and variables from ab, 10, –2x, − 1 and xz .
3 2
2. Observe the following pattern, identify the variable and write the general expression that gives
the cost of pens in terms of the number of pens.
Number of pens 1 2 3 4 ... n

Cost of pens bought for ` 5 each 5 10 15 20 ... ...

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