Question

Calculate the perimeter of a parallelogram with sides 6 3/4 inches and 5 1/2 inches?

Answer 1

`24 1/2` `"in"`

Explanation:

Parallelograms have opposite and congruent sides.

This means that the `4` sides of the parallelogram are

`6 3/4,6 3/4, 5 1/2, 5 1/2`

To find the perimeter, add these all together.

First convert the mixed fractions into improper fractions.

`6 3/4=27/4`

`5 1/2=11/2`

Now, when we add these, we should have a common denominator between

`27/4` and `11/2`

`11/2=22/4`

Now, add the `4` sides:

`27/4+27/4+22/4+22/4=98/4`

`=>49/2=24 1/2` `"in"`

Answer 2

This one is an exercise in fractions which can be done mentally, rather than by the pure application of a method. The fact that the perimeter is asked for is citing the reason to add fractions.

Explanation:

P = `6 3/4 + 5 1/2 + 6 3/4 + 5 1/2`

Work with the whole numbers first, giving: 6+5+6+5 = 22

Now add the fractions: `1/2 + 1/2 = 1` and `3/4 +3/4 = 1 1/2`

So, the perimeter = `22 + 1 + 1 1/2 = 24 1/2`

But, let's look at `3/4 +3/4 = 1 1/2` again.

`3/4 = 1/2 + color(red)(1/4)`

In `3/4 + 3/4` we have `1/2 + color(red)(1/4) + color(red)(3/4)`

The two fractions in red add to make 1, then the `1/2` can be added giving `1 1/2`

Try to work questions like this in your head first, then you can check on paper, or as a last resort, with a calculator.