Question

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Sanya has a piece of land which is in the shape of a rhombus (see Fig. 12.13). She wants her one daughter and one son to work on the land and produce different crops. She divided the land in 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 for their crops? ​

Answer 1

See In the attachment!

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#Siddharth here!

Answer 2

Answer:-

Let ABCD be the field.

Perimeter = 400m

So,each side = 400m ÷ 4 = 100m

$\implies$AB = AD = 100m

Let diagonal BD = 160m

Then Semi-perimeter s of ∆ABD is given by

$s = \frac{100 + 100 + 160}{2} m = 180m$

Therefore,area of ∆ABD

= $\sqrt{180(180-100)(180-100)(180-160)}$

=$\sqrt{180×80×80×20}$m²=4800m²

$\therefore$ Each of them will get an area of 4800m².