Question

Please answer below thx.

Answer 1

24 cm

Explanation:

Since, both the Pentagons are similar. So, their corresponding sides would be in proportion.

Therefore,

`(4)/(4x) = ((x + 2))/(48) \\ \\ (1)/(x) = ((x + 2))/(48) \\ \\ x(x + 2) = 48 \\ \\ {x}^(2) + 2x = 48 \\ \\ {x}^(2) + 2x - 48 = 0 \\ \\ {x}^(2) + 8x - 6x - 48 = 0 \\ \\ x(x + 8) - 6(x + 8) = 0 \\ \\ (x + 8)(x - 6) = 0 \\ \\ x + 8 = 0 \: \: or \: \: x - 6 = 0 \\ \\ x = - 8 \: \: or \: \: x = 6 \\ \\ \because \: x \: cannot \: be \: - ve \\ \implies \: x = 6`

Width of badge = 4x = 4*6 = 24 cm