Question 6104
let x = width of rectangle 1
let 4*x=length (it is 4 times as long as the width) of rectangle 1
area=length*width
area of rectangle 1 = {{{x*4x=4x^2}}}

let x+2 = width of rectangle 2

let 4x+5 = length of rectangle 2
area=length*width
area of rectangle 2=(4x+5)(x+2)={{{4x^2+13x+10}}}

area of rec.2 is 270 cm greater than rec.1
{{{4x^2+13x+10=270+4x^2}}}
subtract {{{4x^2}}} from both sides:
{{{13x+10=270}}}
subtract 10 from both sides:
{{{13x=260}}}
divide both sides by 13:
x=20
now plug this back into your statements:

let x = width of rectangle 1 = 20
let 4*x=length = 80

let x+2 = width of rectangle 2 = 22

let 4x+5 = length of rectangle 2 = 85

to check, get the area of both and find the difference
area 1 = 20*80=1600
area 2 = 22*85= 1870
1870-1600=270, so the answer is correct