Algebra Examples

$(4, 3)$ , $(- 4, - 3)$ , $(- 4, 3)$ , $(4, - 3)$

Step 1

Every rectangle has three different pairs that have the same length. One pair contains the length $l$ , another pair contains the width $w$ , and the last pair contains the diagonal $d$ .

The distance between:

$(4, 3)$ and $(- 4, - 3)$ is $10$

$(4, 3)$ and $(- 4, 3)$ is $8$

$(4, 3)$ and $(4, - 3)$ is $6$

$(- 4, - 3)$ and $(- 4, 3)$ is $6$

$(- 4, 3)$ and $(4, - 3)$ is $10$

$(- 4, - 3)$ and $(4, - 3)$ is $8$

Step 2

The distances between the points show that there are three different pairs that have the same length. One pair contains the length, another pair contains the width, and the last pair contains the diagonal. The diagonal is the longest distance and the width is the shortest distance, which means $l = 8$ and $w = 6$ .

$l = 8$

$w = 6$

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 $P = 2 \cdot (8 + 6)$ . Add the length and the width of the rectangle then multiply the answer by $2$ .

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Step 4.1

Remove parentheses.

$P = 2 \cdot (8 + 6)$

Step 4.2

Simplify $2 \cdot (8 + 6)$ .

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Step 4.2.1

Add $8$ and $6$ .

$P = 2 \cdot 14$

Step 4.2.2

Multiply $2$ by $14$ .

$P = 28$

Step 5

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