Answer:
Length of the rectangular lot = 60 meters
Width of the rectangular lot = 30 meters
Step-by-step explanation:
Let the width of the rectangular lot be x meters.
So, Length of the same = 2x metres.
[tex]A(rectangular \:lot) = (2x)(x)[/tex]
[tex]\implies A(rectangular \:lot) = 2x^2[/tex]
When length is increasEd by 40 m and width by 6 m. Then....
New length = [tex](2x + 40) \:m[/tex]
New width =[tex](x + 6) \:m[/tex]
According to the question:
[tex](2x + 40)(x + 6) = 2(2x^2)[/tex]
[tex]\implies 2x(x + 6) + 40(x + 6) - 4x^2=0[/tex]
[tex]\implies 2x^2+12x + 40x + 240 - 4x^2=0[/tex]
[tex]\implies 2x^2- 4x^2+12x + 40x + 240 =0[/tex]
[tex]\implies -2x^2+52x + 240 =0[/tex]
[tex]\implies 2(x^2-26x - 120) =0[/tex]
[tex]\implies x^2-26x - 120=0[/tex]
[tex]\implies x^2-30x+4x - 120=0[/tex]
[tex]\implies x(x-30)+4(x - 30)=0[/tex]
[tex]\implies (x-30)(x+4)=0[/tex]
[tex]\implies x-30=0,\: x+4=0[/tex]
[tex]\implies x=30,\: x=-4[/tex]
Since, x represents the side length, so its value can't be negative.
[tex]\implies x=30[/tex]
[tex]\implies 2x=2(30)=60[/tex]
Thus,
Length of the rectangular lot = 60 meters
Width of the rectangular lot = 30 meters
