Answer:
The area of the second rectangle is [tex]A=42cm^{2}[/tex]
Step-by-step explanation:
Please see the picture below.
Let´s name the length of the second rectangle as x, so the length of the first rectangle will be 4+x.
The formula of the area of the rectangle is given by
[tex]A=length*width[/tex]
Replacing values:
[tex]96cm^{2}=(4cm+x)*9cm[/tex]
[tex]96cm^{2}=36cm+9cm*x[/tex]
Solving for x:
[tex]96cm^{2}-36cm=9cm*x[/tex]
[tex]60cm=9cm*x[/tex]
[tex]x=\frac{60cm}{9cm}[/tex]
[tex]x=7cm[/tex]
Find the area of the second rectangle:
[tex]A=length*width[/tex]
[tex]A=x*6cm[/tex]
[tex]A=7cm*6cm[/tex]
[tex]A=42cm^{2}[/tex]
