SOLUTION: The length of a rectangle is 1 cm shorter than the diagonal. The length is 2 cm longer than twice the width. Find the perimeter of the rectangle.

Question 983614: The length of a rectangle is 1 cm shorter than the diagonal. The length is 2 cm longer than twice the width. Find the perimeter of the rectangle.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x=width
2x+2=length
diagonal is the hypotenuse of a right triangle
x^2+(4x^2+8x+4)=(2x+3)^2. I squared the width and length and set them equal to the diagonal's length squared
5x^2+8x+4=4x^2+12x+9
x^2+-4x-5=0
(x-5)(x+1)=0
x=5, only reasonable solution.
Width is 5, length is 12, diagonal length is 13 (5-12-13 right triangle)
perimeter is 2 width (10) + 2 length (24)=34 cm.
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