Question

A rhombus-shaped field has green
grass for 18 cows
each side of the rhombus is 30m
and its longer diagonal is 18m, how much area of grass field will each cow be getting .​

Answer 1

✯✯ QUESTION ✯✯

A rhombus-shaped field has green grass for 18 cows each side of the rhombus is 30m and its longer diagonal is 18m, how much area of grass field will each cow be getting..

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✰✰ ANSWER ✰✰

$\implies\tt\bold{a=30m , b=30m , c=48m}$

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

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

$\implies\tt{s=\cancel\dfrac{108}{2}}$

$\implies\tt\bold{s=54m}$

➥Now ,

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

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

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

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

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

$\implies\tt{Area\:of\:Rhombus=ABCD=2\times{432}}$

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

➥Now ,

$\implies\tt{Area\:of\:field\:each\:cow\:get=\cancel\dfrac{864}{18}}$

$\implies\tt\boxed{{48m}^{2}}$

☛So , Each cow will get 48m² of grass field...

Answer 2

Answer:

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Step-by-step explanation:

Let ABCD is a rhombus and length of each side is 30

Length of diagonal AC is 48

From Δ ABC,

Let AB =a =30

AC = b =48

BC = c = 30

Now s = (a+b+c)/2

=> s = (30+48+30)/2

=> s = 108/2

=> s = 54 m

Now area of Δ ABC = √{s*(s-a)*(s-b)*(s-c)}

= √{54*(54-30)*(54-48)*(54-30)}

= √{54*24*6*24}

= √{9*6*24*6*24}

= 3*6*24

= 432 m2

Area of rhombus ABCD = 2*  area of Δ ABC (since area of Δ ABC = area of Δ ACD)

= 2* 432

= 864 m2

Now area of grash for 18 cows = 864 m2

So area of grash for 1 cows = 864/18 m2 = 48 m2