The formula to find the perimeter of a rectangle is
[tex]p = 2(l + w)[/tex]
When we put in our givens to this formula:
[tex]510 = 2 \times (3x + 2x)[/tex]
Combine x values:
[tex]510 = 2 \times 5x[/tex]
Simplify right side:
[tex]510 = 10x[/tex]
Isolate x, by dividing both sides by 10:
[tex]51 = x[/tex]
To find length:
[tex]l = 3x = 3 \times 51 = 153[/tex]
For width:
[tex]w = 2x = 2 \times 51 = 102[/tex]
To solidify our answers:
[tex]p = 2(l + w) = 2 \times (153 + 102) = 2 \times 255 = 510[/tex]
So, our length is 153, our width is 102.
