Question

If you have 36 ft of fencing, what are the bases and side lengths of the different parallelograms you could enclose with the fencing? Consider only whole-number dimensions.

Answer 1

`(l,w) = (1,17)`

`(l,w) = (2,16)`

`(l,w) = (3,15)`

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`(l,w) = (9,9)`

Explanation:

Given

`P = 36ft` --- perimeter

`l \to length`

`w \to width`

Required

Possible dimension of different parallelogram

The perimeter is calculated as:

`P=2(l+w)\\\\\\`

So,we have:

`2(l+w)=36`

Divide by 2

`l + w = 18`

Since l and w must be positive integers, the possible dimensions are:

`(l,w) = (1,17)`

`(l,w) = (2,16)`

`(l,w) = (3,15)`

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`(l,w) = (9,9)`