Question 744996
x = height
2x + 1 = length   {length is 1 more than twice its height}


Area of a rectangle is length x height


x(2x + 1) = 351   {multiplied length x height and set equal to area, 351}
2x² + x = 351
2x² + x - 351 = 0
2x² - 26x + 27x - 351 = 0   {split x into -26x and 27x}
2x(x - 13) + 27(x - 13) = 0   {factored 2x out of 1st two terms and 27 out of last two terms - factoring by grouping}
(2x + 27)(x - 13) = 0  {factored (x - 13) out of the two terms}
2x + 27 = 0 or x - 13 = 0 {set each factor equal to 0}
2x = -27 or x = 13  {subtracted 27 in 1st and added 13 in 2nd}
x = -13.5 or x = 13  {solved each equation for x}
x = 13 {height of a rectangle cannot be negative}
2x + 1 = 27   {substituted 13, in for x, into 2x + 1}


height is 13 cm and length is 27 cm


Perimeter of a rectangle is 2(height) + 2(length)
P = 2(13) + 2(27)   {substituted 13 for height and 27 for length, into perimeter formula}
= 26 + 54   {multiplied}
= 80 {added}


Perimeter of rectangle is 81 cm
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