Question

Sania 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 he divided the land into two equal parts if the perimeter of the land is 400 m and one of the diagonals 160 M how much area each of them will get for their crops

Answer 1

Answer:

4800 m²

Step-by-step explanation:

Given that Sania divided the land, which is in the shape of a rhombus, in two equal parts. Since it is divided in two equal parts, it is likely that it would be divided by the diagonals. We will first find the side of land.

Perimeter of rhombus = 4 × side

→ 400 = 4 × side

→ side = 400/4

→ side = 100 m

Now since the land is to be divide via diagonals, it will be divided into two triangles of equal area, in which two sides would be side of rhombus and third side would be diagonal.

Area of triangle by Heron's formula = $\sqrt{s(s - a)(s-b)(s-c)}$

where, s = semi perimeter of triangle and a, b and c are sides of the triangle.

s = (100 + 100 + 160)/2

s = 180 m

So area = $\sqrt{180(180-160)(180-100)(180-100)} \\\\= \sqrt{180\times20\times80\times80}\\ \\= \sqrt{9\times20\times20\times80\times80}\\ \\= 3 \times 20 \times 80\\\\= 4800$

Hence, each child gets 4800 m² of land for production.

Answer 2

Answer:

I hope it will help you to understanding.