Pre-Algebra Examples

$(1, 4)$ , $(2, 7)$ , $(0, 5)$

Step 1

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

The distance between the three corners is:

$(1, 4)$ and $(2, 7)$ $\to$ $\sqrt{10}$

$(1, 4)$ and $(0, 5)$ $\to$ $\sqrt{2}$

$(2, 7)$ and $(0, 5)$ $\to$ $2 \sqrt{2}$

Step 2

The diagonal is the longest distance and the width is the shortest distance, which means $l = 2.82842712$ and $w = 1.41421356$ .

$l = 2.82842712$

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 $P = 2 \cdot (2.82842712 + 1.41421356)$ . Add the length and the width of the rectangle then multiply the answer by $2$ .

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Step 4.1

Remove parentheses.

$P = 2 \cdot (2.82842712 + 1.41421356)$

Step 4.2

Simplify $2 \cdot (2.82842712 + 1.41421356)$ .

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Step 4.2.1

Add $2.82842712$ and $1.41421356$ .

$P = 2 \cdot 4.24264068$

Step 4.2.2

Multiply $2$ by $4.24264068$ .

$P = 8.48528137$

Step 5