Algebra - Class 6 - Mathematics
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Exercise 11.1 - Algebra | NCERT | Mathematics | Class 6
ind the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
(a) A pattern of letter $T$ as -|
(b) A pattern of letter $\mathrm{Z}$ as -/-
(c) A pattern of letter $U$ as |_|
(d) A pattern of letter $\mathrm{V}$ as \/
(e) A pattern of letter $\mathrm{E}$ as $|\overline{\_}$ -
(f) A pattern of letter $S$ as -|-|-
(g) A pattern of letter $A$ as /-\
We already know the rule for the pattern of letters L, C and F. Some of the letters from Q. 1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
To find the rule for the number of matchsticks required to make the given matchstick patterns for each letter, let's analyze the construction of each letter individually and then determine which of them share the same rule as the pattern of the letter L.
(a) A pattern of letter T as -|
The pattern of letter T requires 2 matchsticks: 1 for the horizontal part and 1 for the vertical part.
(b) A pattern of letter Z as -/-
The pattern of letter Z requires 3 matchsticks: 2 for the horizontal parts and 1 for the diagonal part.
(c) A pattern of letter U as |_|
The pattern of letter U requires 3 matchsticks: 2 for the vertical parts and 1 for the bottom part.
(d) A pattern of letter V as /
The pattern of letter V requires 2 matchsticks: both for the diagonal parts.
(e) A pattern of letter E as $|\overline{_}$ -
The pattern of letter E requires 4 matchsticks: 1 for the vertical part and 3 for the horizontal parts.
(f) A pattern of letter S as -|-|-
The pattern of letter S requires 5 matchsticks: 2 for the vertical parts and 3 for the horizontal parts.
(g) A pattern of letter A as /-\
The pattern of letter A requires 3 matchsticks: 2 for the diagonal parts and 1 for the horizontal part.
Analysis of Same Rule as L
Without the specific rule for the letter L provided, we'll make an assumption based on conventional representation. The letter L typically requires 2 matchsticks: 1 vertical and 1 horizontal. Looking at the list:
- Letter T: Requires 2 matchsticks similar to L, though structured differently.
- Letter V: Requires 2 matchsticks; however, these are diagonal rather than one vertical and one horizontal.
- Other Letters: Do not fit the assumption if L requires specifically 1 vertical and 1 horizontal.
The fundamental reason some letters share the same rule (based on matchstick count) with L is essentially about the total matchstick count and not the orientation or arrangement of these sticks. Thus, any letter that requires 1 vertical and 1 horizontal pattern to be constructed could share the "rule" with L, if we interpret the rule strictly as the count of matchsticks required. However, if the orientation or specific arrangement of matchsticks in L is a part of the "rule", then none of the patterns perfectly model after L as each has a unique arrangement or orientation of matchsticks.
Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use $n$ for the number of rows.)
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Sign up nowIf there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use $b$ for the number of boxes.)
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Sign up nowThe teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use $s$ for the number of students.)
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Sign up nowA bird flies 1 kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use $t$ for flying time in minutes.)
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Sign up nowRadha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for $r$ rows? How many dots are there if there are 8 rows? If there are 10 rows?
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Sign up nowLeela is Radha's younger sister. Leela is 4 years younger than Radha. Can you write Leela's age in terms of Radha's age? Take Radha's age to be $x$ years.
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Sign up nowMother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is $l$, how many laddus did she make?
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Sign up nowOranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be $x$, what is the number of oranges in the larger box?
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Sign up now(a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)
Shape (a) is a square with 4 matchsticks.
Shape (b) is two squares with 7 matchsticks
Shape (c) continues this pattern, and is 3 squares
Shape (d) further adheres to this rule,
(b) Fig 11.7 gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.
Shape (a) is a Triangle with 3 matchsticks.
Shape (b) is two Triangles with 5 matchsticks
Shape (c) continues this pattern, and is 3 Triangles
Shape (d) further adheres to this rule,
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