the length of a rectangle, I, is six meters more than its width, w. if the perimeter of the rectangle is 36 meters, what is the length of the rectangle, in meters?

Question

anonymous · Answer

Using P as perimeter, l as length and W and width:
For a rectangle:
$$P = 2 l + 2 w$$
But they tell us that the lenght is six meters more than its width. We write that in this manner:
$$l = w+6$$
If we replace the first l for this one, we will end up with
$$P = 2 (w+6) + 2w$$
$$P = 2 w+12 + 2w$$
$$P = 4w + 12$$
And since we know the perimeter is 36,
$$36 = 4w + 12$$
$$4w = 24$$
$$w = 6$$

But they ask us the length. So going back, we remember that l = w + 6. Since w is 6, l must be 12.

anonymous · Answer

so its A