Question

The perimeter of a rectangle is 510 cm. The ratio of the length to the width is 3:2. What are the dimensions of this rectangle?

Answer 1

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