Question

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


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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.

Formula used:

$\\\bigstar \: {\underline{\boxed{\bf{\red{s=\dfrac{a+b+c}{2}}}}}}$

where,

• a = 30m
• b = 30m
• c = 48m

$\\\bigstar \: {\underline{\boxed{\bf{\red {area=\sqrt{s(s-a)\:(s-b)\:(s-c)}}}}}}$

Solution:

we know that,

$\\\dashrightarrow\sf \: \: {s=\dfrac{a+b+c}{2}}$

★ Substituting values from the above formula :

$\\\dashrightarrow\sf{s=\dfrac {30+30+48}{2}}$

$\dashrightarrow\sf \: \: {\cancel\dfrac{108}{2}}$

$\dashrightarrow\bold \red { \: \: 54m}$

Now ,

again we know that,

$\\\sf\dashrightarrow{Area= \sqrt{s(s-a)\:(s-b)\:(s-c)}}$

★ Substituting values from the above formula :

$\\\sf\dashrightarrow{\sqrt{54 (54-30)\:(54-30)\:(54-48)}}$

$\dashrightarrow\sf{\sqrt{54\times{24}\times{24}\times{6}}}$

$\sf\dashrightarrow{\sqrt{2 \times{3}\times{3}\times{3}\times{2}\times{2}\times{2}\times{3}\times{2}\times{2}\times{3}\times{2}\times{3}\times{2}\times{3}}}$

$\dashrightarrow\bold \blue {432{m}^{2}}$

★Area of Rhombus ABCD :

• $\dashrightarrow\sf{ \: \: 2\times{432}}$
• $\dashrightarrow\bold \green{ \: 864 \: {m}^{2}}$

★Area of Field each cow will get :

• $\\\dashrightarrow\sf{ \: \: \cancel\dfrac{864}{18}}$
• $\dashrightarrow\sf\bold \pink {48 \: {m}^{2}}$

So , Each cow will get 48m²

Answer 2

the answer is : Each cow will get 48m²