Question

a single square is made from 4 match sticks to make two square in a row take 7 match sticks while three squares in a row take 10 matchsticks if there are 109 match sticks calcuta the number of squares in the row

Answer 1

Answer:

36 squares

Step-by-step explanation:

4 stick for 1 square (3+1 sticks)

7 sticks for 2 squares (additional 3 for 2nd square)

10 sticks for 3 square ( additional 3 for next square)

Other than 1st square every square need 3 sticks so

Sticks required for n squares = 3n+1

3n+ 1 = 109

3n = 108

n = 36

Answer 2

Answer:

36

Step-by-step explanation:

From the given information it is clear that

The number of match sticks required to make a square = 4

The number of match sticks required to make 2 squares = 7

The number of match sticks required to make 3 squares = 10

From the given pattern it is clear that we need 3 addition match sticks to make an additional square box after first box.

For x square boxes the number of required match sticks is

$N=4+3(x-1)$

Let x be the number of square boxes that are made by using 109.

$4+3(x-1)=109$

$4+3x-3=109$

$1+3x=109$

Subtract 1 from both sides.

$3x=109-1$

$3x=108$

Divide both sides by 3.

$x=\frac{108}{3}$

$x=36$

Therefore, 36 square can be formed by using 109 match sticks.