SOLUTION: Area of original rectangle is 12 x²+11x-5f t² Area is changed by decreasing the length by 2ft and increasing the width by 4ft. Find the new area *remember the length is always

Algebra ->  Rectangles -> SOLUTION: Area of original rectangle is 12 x²+11x-5f t² Area is changed by decreasing the length by 2ft and increasing the width by 4ft. Find the new area *remember the length is always       Log On


   

Question 1137426: Area of original rectangle is 12 x²+11x-5f t² Area is changed by decreasing the length by 2ft and increasing the width by 4ft. Find the new area
*remember the length is always the longer side.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Area of original rectangle is
12x%5E2%2B11x-5....factor completely to find expressions for length and width
12x%5E2-3x%2B15x-5
%2812x%5E2-4x%29%2B%2815x-5%29
4x%283x-1%29%2B5%28x-1%29
%283x+-+1%29+%284+x+%2B+5%29
let
%283x+-+1%29=> be the length
%284+x+%2B+5%29=> be the width

Area is changed by:

decreasing the length by 2 ft =>%283x+-+1-2%29=>%283x+-+3%29
and increasing the width by 4 ft=>%284+x+%2B+5%2B4%29=>%284+x+%2B+9%29
the new area is:
%283x+-+3%29%284+x+%2B+9%29.....expand
12+x%5E2+%2B+15+x+-+27


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Area of original rectangle is 12 x²+11x-5f t² Area is changed by decreasing the length by 2ft and increasing the width by 4ft. Find the new area
*remember the length is always the longer side.
Factoring the trinomial results in: (4x + 5)(3x - 1).

Looking at both expressions/binomials, it's OBVIOUS that 4x + 5 is UNEQUIVOCALLY the LARGER EXPRESSION,

and so, when the adjustments to the dimensions are made, we get the following trinomial for the ADJUSTED area: 

ACCEPT no other answer! 



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