A farmer has a rectangular field with a length of 30 yards and width of x yards. If the perimeter is the sum of all four sides of the field, wow do you write an expression for the perimeter of the field, in yards?

Dec 13, 2015

The expression for the perimeter of the field is $60 + 2 x$ yards.

Explanation:

The formula to find the perimeter of a rectangle is

$P = 2 \left(l\right) + 2 \left(w\right)$

$P$ stands for perimeter, $l$ stands for length, and $w$ stands for width.

There is a good reason why this is the formula for the perimeter of a rectangle.

In a rectangle, two of the sides have the same length, and two of the sides have the same width. Therefore, we add those two pairs of sides up, and we get the perimeter.

Using the length and width provided, we can insert those values into our perimeter formula:

$P = 2 \left(30 \setminus y a r \mathrm{ds}\right) + 2 \left(x \setminus y a r \mathrm{ds}\right)$

This simplifies to:

$P = 60 \setminus y a r \mathrm{ds} + 2 x \setminus y a r \mathrm{ds}$

or simply:

$P = 60 + 2 x \setminus y a r \mathrm{ds}$