Question

find the rule which gives the number of matchsticks required to make the following patterns -
1) A pattern of letter 'H'
2)A pattern of letter 'V'

please give correct answer ​

Answer 1

Sum of angles of a quadrilateral = 360°

Their ratio = 2 : 4 : 5 : 7

Let first angle = 2x

then second angle = 4x

third angle = 5x

and fourth angle = 7x

∴ 2x + 4x + 5x + 7x = 360°

=> 18x = 360°

=> x = \(\frac { { 360 }^{ o } }{ 18 } \) = 20°

Hence, first angle = 2x = 2 x 20° = 40°

Second angle = 4x = 4 x 20° = 80°

Third angle = 5x = 5 x 20° = 100°

and fourth angle = 7x = 7 x 20° = 140°Ans.