The dimensions of a rectangle are 2x + 1 and x - 1. if each dimension is increased by 2 units, write and simplify an expression that represents the increase in area.
2007-12-22 23:43:25 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A1 = (2x + 1) (x - 1)
A2 = (2x + 3) (x + 1)
Increase = (2x + 3)(x+ 1) - (2x + 1)(x - 1)
Increase = 2x² + 5x + 3 - 2x² + x + 1
Increase = 6x + 4
2007-12-23 00:02:43 · answer #1 · answered by Como 7 · 1⤊ 1⤋
Area using first Dimension,
A1 = (2x + 1) * (x - 1) = 2(x^2) -2x + x -1 = 2(x^2) - x -1
Increased dimensions are
L1= (2x +1 +2) = (2x +3)
L2= (x - 1 + 2) = (x + 1)
Area after increasing each dimension
A2 = (2x + 3) * (x + 1) = 2(x^2) + 2x + 3x +3 = 2(x^2) +5x +3
Increase in area
A = A2 - A1 = [ 2(x^2) + 5x + 3 ] - [ 2(x^2) - x -1 ]
A = 2(x^2) + 5x +3 - 2(x^2) + x + 1 = 6x +4
So answer is "6x +4"
2007-12-23 08:46:07 · answer #2 · answered by Solid Snake 1 · 0⤊ 1⤋
New Area = (2x+1+2)(x-1+2)
= (2x+3)(x+1)
Old Area = (2x+1)(x-1)
Difference = (2x^2+5x+3) - (2x^2-x-1)
= 2x^2+5x+3-2x^2+x+1
= 6x+4
2007-12-23 08:00:28 · answer #3 · answered by stanschim 7 · 0⤊ 1⤋
original Area = (2x+1)(x-1)
New Area = (2x+3)(x+1)
Increase in Area = ( (2x+3)(x+1) - (2x+1)(x-1) )
Increase in Area = ( 2x²+5x+3 - (2x²-x-1) )
Increase in Area= 6x+4
2007-12-23 07:59:56 · answer #4 · answered by Murtaza 6 · 0⤊ 0⤋
The area is (2x+1)(x-1)=2x^2-x-1
After the increase the area will be
(2x+3)(x+1)=2x^2+5x+3
The difference is
(2x^2+5x+3)-(2x^2-x-1)=6x+4
2007-12-23 07:55:11 · answer #5 · answered by fhtagn 4 · 1⤊ 1⤋