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The area of a rectangle is given by the formula: A = lw
Given that its length is 3m more than thrice its width you'll have:
l = 3w + 3 -----equation1
and
A = 65m²
Substitute everything to the area formula you'll have:
A = lw65m² = (3w + 3 ) (w)
65 = 3w² + 3w or
3w² + 3w - 65 = 0
using quadratic formula you'll have:
[tex]w = \frac{-b (+-) \sqrt{b^2-4ac} }{2a} \\ w = \frac{-3(+-) \sqrt{3^2-4(3)(-65)} }{2(3)} \\ w = \frac{-3 (+-) \sqrt{789} }{6} \\ w= \frac{-3 + \sqrt{789} }{6} = 4.1815; \\ w= \frac{-3- \sqrt{789} }{6}=-5.1815 [/tex]
take the positive value since there's no negative length.
w = 4.1815m
substitute to equation 1
l = 3w + 3
l = 3(4.1815) + 3
l = 15.5445m
Since you are asked of the perimeter then you'll have the formula for perimeter of a rectangle used.
P = 2l + 2w
Substituting you'll have:
P = 2 (15.5445) + 2(4.1815)
P = 39.452meters