Answer:
18 cm
Step-by-step explanation:
Let the width of the rectangle be x cm, then the length of the rectangle is x+5 cm.
The area of the ractangle is
[tex]x\cdot (x+5)\ cm^2.[/tex]
The area of the square with side's length of x cm is
[tex]x^2\ cm^2.[/tex]
The area of the square with side's length of x+5 cm is
[tex](x+5)^2\ cm^2.[/tex]
The area of constructed figure is
[tex]x(x+5)+2x^2+2(x+5)^2\ cm^2.[/tex]
Since the total area of the constructed figure is 120 cm², you have
[tex]x(x+5)+2x^2+2(x+5)^2=120.[/tex]
Solve this equation:
[tex]x^2+5x+2x^2+2x^2+20x+50=120,\\ \\5x^2+25x-70=0,\\ \\x^2+5x-14=0,\\ \\D=5^2-4\cdot (-14)=25+56=81,\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{81}}{2}=-7,\ 2.[/tex]
The width of the rectangle cannot be negative, so x=2 cm and x+5=7 cm and the perimeter of the rectangle is
[tex]2x+2(x+5)=2\cdot 2+2\cdot 7=4+14=18\ cm.[/tex]
