Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops to suffice the needs of their family. She divided the land in two equals parts. If the perimeter of the land is `400 m` and one of the diagonals is `160 m ,` how much area each of them will get?

Explanation

Let `ABCD` is the field.
each side be,`x`.
Perimeter of the field`=4x`
Given perimeter`=400m`
`=>4x=400m`
`=>x=100m`
Length of the diagonal, `BD=160m`
In `/_\ABD,AB=100m`
`AD=100m \and\ BD=160m`
`=>s=1/2(100+100+160)=180m`
Area of `/_\ABD=sqrt(s(s−a)(s−b)(s−c))`
`=sqrt(180(180-100)(180-100)(180-160)`
`=sqrt(9xx20xx80xx80×x20`
`=3×20×80`
`=4800m^2`
Since,`ABCD`is a rhombus and diagonal divides it into two congruent triangle
Therefore, each of them will get an area `4800 m^2`