Question

The area of a parallelogram and a square are the same. If the perimeter of the square is 160m and the height of the parallelogram is 20m, what is the length of the corresponding base of the parallelogram?

Answer 1

`80` meters

Explanation:

Area of a parallelogram: `bh` (`b` is the base, `h` is the height)

Perimeter of a square: `4s` (`s` is the side length)

Area of a square: `s*s` or `s^2`

The perimeter of the square is `160` meters:

`4s=160`

`s=40 rarr` Each side length is 40 meters

That means the area of the square is `40*40`, or `1600`

Since the areas of the square and parallelogram are the same, the base of the parallelogram (`b`) multiplied by the height (`20`) has to be `1600` as well.

`20b=1600`

`b=80`