Hey, CadenClough! For this, it's best to use algebra. We know that rectangles have two of each measure: two lengths and two widths. This means the formula to find the complete perimeter of the rectangle is 2l + 2w = p.
Now let's look at the problem. For length, we have x + 3 and for width we have 2x - 6. First off, fill in the values for length and width in the perimeter equation like this:
[tex]2(x + 3) + 2(2x - 6) = 26[/tex]
Now distribute the 2:
[tex]--> 2x + 6 + 4x - 12 = 26[/tex]
Combine like terms:
[tex]2x + 4x + 6 - 12 = 26[/tex]
Simplify:
[tex]6x - 6 = 26[/tex]
Isolate x:
[tex]6x = 26 + 6[/tex]
--> [tex]x = \frac{32}{6}[/tex]
Now plug in the value of x:
[tex]2(\frac{32}{6} + 3) + 2(2 * \frac{32}{6} - 6)[/tex]
= 64/3 - 12 + 32/3 + 6
= 26
So x = [tex]\frac{32}{6}[/tex] or 16/3.
