Answer:
Length of sandbox (3w + 1) = 9.1 m
Width of sandbox = 2.7 m
Step-by-step explanation:
[tex]w(3w + 1) = {5}^{2} \\ \\ 3 {w}^{2} + w = 25 \\ \\ 3 {w}^{2} + w - 25 = 0 \\ \\ equating \: it \: with \\ \\ a {x}^{2} + bx + c = 0 \\ \\ a = 3 \\ b = 1 \\ c = - 25 \\ \\ {b}^{2} - 4ac \\ = {1}^{2} - 4 \times 3( - 25) \\ \\ = 1 + 300 \\ \\ = 301 \\ \\ w = \frac{ - 1 \pm \sqrt{301} }{2 \times 3} \\ \\ w = \frac{ - 1 \pm 17.3493516 }{6} \\ \\ w = \frac{ - 1 \pm 17.3493516 }{6} \\ \\ considering \: only \: + ve \: sign \\ \\ w = \frac{ - 1 + 17.3493516 }{6} \\ \\ w = \frac{16.3493516 }{6} \\ \\ w = 2.72489193 \\ \\ w = 2.7 \: m[/tex]
3w + 1 = 3*2.7 + 1 = 8.1 + 1 = 9.1 m
