How do I find the length and width of a rectangle whose perimeter is 43 inches?

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Actually, you cannot.

Any rectangle has four sides, two pairs of which have equal length. If we denote the length of one side as x (inches), then one more side has the same length, and two remaining sides have length y each.

Perimeter, the sum of all side's lengths, is clearly

`2x + 2y = 43.`

There are many (infinitely many) combinations of x and y. For any y between 0 and 43/2 = 21.5 we can find x,

`x = 21.5 - y.`

(or for any such x find y).

To find both x and y we need one more condition. For example, if area of a rectangle is given, or ratio of side's lengths, or diagonal length, or so. In such case we have a system of two equations of two variables which often have one solution.