Question

18)A rhombus shaped field has green grass for 18 cows to graze.If each side of the rhombus is 30m and its longer diagonal is 48m,how much area of grass field will each cow be getting ? *

48m²

40m²

46m²

none

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Answer 1

Given :

• Each side of Rhombus is 30m.
• Diagonal of Rhombus is 48m.

To Find :

• Area of grass field each cow will get.

Solution :

• a = 30m
• b = 30m
• c = 48m

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

$\longmapsto\tt{s=\dfrac{30+30+48}{2}}$

$\longmapsto\tt{\cancel\dfrac{108}{2}}$

$\longmapsto\tt\bold{54m}$

Now ,

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

$\longmapsto\tt{\sqrt{54(54-30)\:(54-30)\:(54-48)}}$

$\longmapsto\tt{\sqrt{54\times{24}\times{24}\times{6}}}$

$\longmapsto\tt{\sqrt{2\times{3}\times{3}\times{3}\times{2}\times{2}\times{2}\times{3}\times{2}\times{2}\times{3}\times{2}\times{3}\times{2}\times{3}}}$

$\longmapsto\tt\bold{432{m}^{2}}$

_______________________

Area of Rhombus ABCD :

$\longmapsto\tt{2\times{432}}$

$\longmapsto\tt\bold{864{m}^{2}}$

Area of Field each cow will get :

$\longmapsto\tt{\cancel\dfrac{864}{18}}$

$\longmapsto\tt\bold{48{m}^{2}}$

So , Each cow will get 48m²