Q. 254.4( 22 Votes )

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 into two equal 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?

Answer :

To Find: Area of land each son and daughter have.

Given: Perimeter of land = 400 m


One of the diagonals = 160 m


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Diagram:



Explanation:


ABCD is the field, and it is divided by the diagonal BD = 160 m into two equal parts.


The perimeter of rhombus = 400 m


4 × side = 400 m


Side = 100 m


Now, the area of Δ ABD and Δ BDC are equal.


Let us calculate the area of Δ ABD




s = 180 m




Area = 4800 m2.


Hence, each of the children of Sanya will get 4800 m2 of land.


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