Answers

2015-07-19T12:36:57+08:00

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:

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

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

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