Question

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Answer 1

Answer:

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Answer 2

$\large\underline{\underline{\text{Question:}}}$

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

$\large\underline{\underline{\text{Solution:}}}$

Let we divide the rhombus in two triangles.

As we know that,

• All sides of a rhombus are equal.

So,

• $AB = BC$
• $AD = CD$

So We can say that,

• Both triangles are Isosceles ∆.

Finding the area of each ∆,

• $\text{The equal side }(a) = 30m$
• $\text{The unequal side }(b) = 48m$

As we know that,

$\longrightarrow \boxed{ \text{Area}_{(\text{Isosceles} \: \triangle)} = \frac{b}{4} \sqrt{4 {a}^{2} - {b}^{2} } }$

$\longrightarrow \text{Area}_{( \text{Isosceles} \: \triangle)} = \bigg \{\frac{48}{4} \sqrt{4 {(30)}^{2} - {(48)}^{2} } \bigg \} {m}^{2}$

$\longrightarrow \text{Area}_{(\text{Isosceles} \: \triangle)} = \bigg \{12 \sqrt{4 {(900)} - 2304 } \bigg \} {m}^{2}$

$\longrightarrow \text{Area}_{(\text{Isosceles} \: \triangle)} = \bigg \{12 \sqrt{3600 - 2304 } \bigg \} {m}^{2}$

$\longrightarrow \text{Area}_{(\text{Isosceles} \: \triangle)} = \bigg \{12 \sqrt{1296} \bigg \} {m}^{2}$

$\longrightarrow \text{Area}_{(\text{Isosceles} \: \triangle)} = 12 \times 36 {m}^{2}$

$\longrightarrow \boxed{ \text{Area}_{(\text{Isosceles} \: \triangle)} = 432 {m}^{2}}$

As we assumed that,

$\longrightarrow \text{Area}_{( \text{Rhombus})} = 2 \bigg( \text{Area}_{(\text{Isosceles} \: \triangle)} \bigg)$

$\longrightarrow \text{Area}_{( \text{Rhombus})} = 2 (432 {m}^{2})$

$\longrightarrow \boxed{ \text{Area}_{( \text{Rhombus})} = 864 {m}^{2} }$

We know that,

$\longrightarrow \boxed{\text{Area getting each cow} = \frac{\text{Area}_{( \text{Rhombus})}}{ \text{No. of Cows}}}$

$\longrightarrow \text{Area getting each cow} = \frac{432 {m}^{2} }{18}$

$\longrightarrow \boxed{ \text{Area getting each cow} = 48 {m}^{2}}$

$\large\underline{\underline{\text{Required Answer:}}}$

• The Area grazed by each cow is 48m².