Question

Santa has a piece of land which is the shape of a rhombus .she wants herb one daughter and one son to work on the land and produce different crops .she divide the land into two equal parts .If the perimeter of the land is 400m and one of the diagonal is 160m, how much area of them will get for their crops .

Answer 1

Given :

• Perimeter of Land = 400m
• One Diagonal = 160m

To Find :

• Area each (son and daughter) will get.

Solution :

$\longmapsto\tt{Perimeter=400m}$

In Δ BCD :

• a = 100m
• b = 100m
• c = 160m

Now :

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{100+100+160}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{360}{2}=180m}$

$\longmapsto\tt\bold{s=180m}$

_______________________

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{180(180-100)(180-100)(180-160)}}$

$\longmapsto\tt{\sqrt{180\times{80}\times{80}\times{20}}}$

$\longmapsto\tt\bold{4800{m}^{2}}$

So , Each of them will get 4800m² of Area..