Answer:
[tex]x=13[/tex]
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:
[tex]P=2l+2w[/tex]
Where l is the length and w is the width.
We know that the perimeter is 80. Looking at the rectangle, we can also see that the length is 2x+3 while the width is x-2. Thus, make the substitutions:
[tex]P=2l+2w\\80=2(2x+3)+2(x-2)[/tex]
Distribute:
[tex]80=4x+6+2x-4[/tex]
Combine like terms and add:
[tex]80=6x+2[/tex]
Subtract 2 from both sides:
[tex]78=6x[/tex]
Divide both side by 6:
[tex]x=13[/tex]
Thus, the value of x is 13.
