Perimeter of a Rectangle Example
Below is a geometry question using
the perimeter of a rectangle. In a geometry problem,
you may be given the perimeter of a rectangle and the
relationship between its width and length. With the perimeter
of a rectangle known, you are supposed to calculate the other
dimensions of the rectangle.
Using the perimeter of the rectangle to find
the other dimensions is a common geometry problem. The example
below has the perimeter of a rectangle as 62 inches. However,
the same method works whatever the perimeter of the rectangle
is and whatever the relationship between its width and length
is.
Perimeter of a Rectangle Example: finding
width and length of the rectangle
Suppose the perimeter of a rectangle is 62
inches. Let's also suppose that you also know that the
length of the rectangle is 1 inch more than twice the width of
the rectangle. The geometry question would be, what are the
dimensions (i.e. width and length) of the rectangle?
The diagram of the rectangle above marks the
length (L) and width (W) of the rectangle. Since we
are told that the length (L) is 1 inch more than twice the
width, the length is given by L = 2W + 1 (shown in red).
We know from the formula of
the perimeter of a rectangle that the perimeter
formula is:
Since we know L in terms of W, we are going
to substitute L so that we have an algebraic equation with only
one unknown, W.
Now we know the width of the rectangle, W,
is 10 inches. L is 2W + 1 which gives 21 inches. You can double
check your results by putting W and L back in the perimeter of
the rectangle equation. The perimeter is 2 (10 + 21) = 62
inches which is what you started with. So, you know that
you have done the calculation right.
