Question

5. A rhombus-shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and
its longer diagonal is 48 m, how much area of grass field will each cow be getting?
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Answer 1

Step-by-step explanation:

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Answer 2

Given :

• A rhombus shaped field has green grass for 18 cows to graze

• Each side of rhombus is 30 m

• Longer diagonal is 48 m

To Find :

• Area of grass field each cow be getting

Solution :

Draw a rhombus ABCD. Now,Clearly ∆ ABC and ∆ ADC are congruent.

$\therefore$ Area of ∆ ABC = Area of ∆ ADC

Also, triangles ABC and ADC hace equal perimeters.

Let the semi-perimeter of ∆ ABC and ∆ ADC be s

Then,

$\bigstar \: \boxed{ \sf \: Semi-Perimeter = \frac{ Sum \: of \: all \: sides}{2} }$

$\longrightarrow \sf \: s = \dfrac{30 + 30 + 48}{2} \: m$

$\longrightarrow \sf \: s = \cancel\dfrac{108}{2} \: m$

$\longrightarrow \sf \red{s = 54 \: m}$

Now, Let's Find Area of ∆ ABC

→ Area of ∆ ABC = Area of ∆ ADC

Applying Heron's Formulae :

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

$\longrightarrow \sf \: \sqrt{54(54 - 30)(54 - 30)(54 - 48)} {m}^{2}$

$\longrightarrow \sf \: \sqrt{54 \times 24 \times 24 \times 6} \: {m}^{2}$

$\longrightarrow \sf \: \red{ \sf \: 432 {m}^{2} }$

Now,

$\bigstar \: \boxed{ \sf \: Area \: of \: rhombus \: ABCD = 2 \times \: Area \: of \: \triangle \: ABC}$

$\longrightarrow \sf \: 2 \times 432 {m}^{2}$

$\longrightarrow \red{\sf \: 864 {m}^{2} }$

Area of grass field each cow will graze

$\longrightarrow \sf \: \dfrac{Area \: of \: field }{Cow}$

$\longrightarrow \sf \: \cancel \dfrac{864}{18}$

$\longrightarrow \red{\sf 48 {m}^{2} }$

$\therefore$ Each cow will graze 48m² area of grass field.