Question
Construct line segments whose lengths are: $12\ cm\ 5mm$
✓
Answer
Draw a line $L$ on the paper and mark a point $A$ on it.
Take a compass and place its metal point at zero mark of the ruler.
Adjust the compass such that the pencil point gets placed at the point which is $5$ small points from the mark of $12\ cm$ to $13\ cm$ of the ruler. Now, take the compass to $L$ such that its metal point is on $A$.
Mark a small mark at $B$ on $L$ corresponding to the pencil point of the compass.
$ AB$ is the required line segment of $12\ cm$ $5mm.$
Take a compass and place its metal point at zero mark of the ruler.
Adjust the compass such that the pencil point gets placed at the point which is $5$ small points from the mark of $12\ cm$ to $13\ cm$ of the ruler. Now, take the compass to $L$ such that its metal point is on $A$.
Mark a small mark at $B$ on $L$ corresponding to the pencil point of the compass.
$ AB$ is the required line segment of $12\ cm$ $5mm.$
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Study the following pattern:
$1 + 3 = 2 \times 2$
$1 + 3 + 5 = 3 \times 3$
$1 + 3 + 5 + 7 = 4 \times 4$
$1 + 3 + 5 + 7 + 9 = 5 \times 5$
By observing the above pattern, find
$i.\ 1 + 3 + 5 + 7 + 9 + 11$
$ii.\ 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15$
$iii.\ 21 + 23 + 25 + ......+ 51$
→$1 + 3 = 2 \times 2$
$1 + 3 + 5 = 3 \times 3$
$1 + 3 + 5 + 7 = 4 \times 4$
$1 + 3 + 5 + 7 + 9 = 5 \times 5$
By observing the above pattern, find
$i.\ 1 + 3 + 5 + 7 + 9 + 11$
$ii.\ 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15$
$iii.\ 21 + 23 + 25 + ......+ 51$