Question

In the given figure, observe the matchstick pattern and fill in the table that follows:

Answer 1

Explanation:- We can determine a pattern from the image to find the number of matchsticks required for making a fixed number of rectangles.

From the image, we can see the after the 1st rectangle (which need 4 matchsticks) we need only 3 matchsticks to make another rectangle.

So, for making 2 rectangles,

we need, $4+3\times 1=4+3=7matchsticks$

So, for making 3 rectangles,

we need, $4+3\times 2=4+6=10matchsticks$

So, for making 4 rectangles,,

we need, $4+3\times 3=4+9=13matchstikcs$

So, for making 5 rectangles,

we need, $4+3\times 4=4+12=16matchsticks$

So, for making 10 rectangles,

we need, $4+3\times 9=4+27=31matcsticks$

Therefore, the required table is given as-

Number of Rectangles(s)	1	2	3	4	5	10
Number of matchsticks	4	7	10	13	16	31