Length = 3w + 3, width = w
The area of a rectangle is length * width so:
65 = (3w+3)w
65 = 3w² + 3w
0 = 3w² + 3w - 65
We use the quadratic formula
w = -3 ± √[3²+4(3)(65)] = -3 ± √[9+780] = -3 ± √789
6 6 6
We only get the positive value.
Perimeter = 2(length + width)
Length = 3 (-3 + √789) + 3 = -3 + √789 + 3 = 3 + √789
6 2 2
Perimeter = 2 ( 3 + √789 + -3 + √789 ) = 2 ( 9 + 3√789 -3 + √789 )
2 6 6
= 6 + 4√789 m
3
