Find the Square or Rectangle Perimeter

$(1, 3)$ , $(3, 3)$ , $(3, 1)$

Step 1

The distances between the given points are the length (l), width (w), and diagonal (d).

The distance between the three corners is:

$(1, 3)$ and $(3, 3)$ $\to$ $2$

$(1, 3)$ and $(3, 1)$ $\to$ $2 \sqrt{2}$

$(3, 3)$ and $(3, 1)$ $\to$ $2$

Step 2

The diagonal is the longest distance and the width is the shortest distance, which means $l = 2$ and $w = 2$ .

$l = 2$

Step 3

The perimeter of a rectangle is $P = 2 \cdot (l + w)$ .

$P = 2 \cdot (l + w)$

Step 4

In this case, the perimeter is $P = 2 \cdot (2 + 2)$ . Add the length and the width of the rectangle then multiply the answer by $2$ .

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Step 4.1

Remove parentheses.

$P = 2 \cdot (2 + 2)$

Step 4.2

Simplify $2 \cdot (2 + 2)$ .

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Step 4.2.1

Add $2$ and $2$ .

$P = 2 \cdot 4$

Step 4.2.2

Multiply $2$ by $4$ .

$P = 8$

Step 5

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Find the Square or Rectangle Perimeter

Analytic Geometry

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