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?

Answer 1

$Hey\:!!..$

The answer goes here....

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》To find :

How much area of grass field will each cow be getting ?

》Given :

Let us take the field to be ABCD.

Side of rhombus, AB = BC = CD = DA = 30 m

Diagonal, BD = 48 m

》Solution :

Area of the rhombus = Area of $\triangle ABD$ + Area of $\triangle BCD$

So, Area of $\triangle ABD$ -

Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Here, a = 30 m, b = 30 m and c = 48 m.

Now, s = $\frac{a+b+c}{2}$

⟹ $\frac{30+30+48}{2}$ = 54 m

So, using the formula,

⟹ $\sqrt{54(54-30)(54-30)(54-48)}$

⟹ $\sqrt{54(24)(24)(6)}$

⟹ $\sqrt{(6\times 9)(24\times 24)(6)}$

⟹ $\sqrt{{6}^{2}\times {3}^{3}\times {24}^{24}}$

⟹ $6\times 3\times 24$

⟹ $432\:{m}^{2}$

So, the area of $\triangle ABD$ is  $432\:{m}^{2}$ .

Also, the area of $\triangle BCD$ will be same since both the triangle have equal sides.

So, the area of $\triangle BCD$ is $432\:{m}^{2}$ .

Now, Area of the rhombus = Area of $\triangle ABD$ + Area of $\triangle BCD$

⟹ $432\:{m}^{2}$ + $432\:{m}^{2}$

⟹ $864\:{m}^{2}$

So, the area of the rhombus is  $864\:{m}^{2}$ .

Now, the area for 18 cows to graze the field is equal to the area of rhombus. So, area for 1 cow -

⟹ $\frac{864}{18}$

⟹  $48\:{m}^{2}$

So, the area for one cow to graze will be  $48\:{m}^{2}$ .

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Thanks !!..

Answer 2

$\huge{\bold{\underline{\underline{Heya}}}}$
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•Let the rhombus shaped field be ABCD

Given:-

⏩side of rhombus=30m

◻️As we know that ,

◻️All sides of rhombus are equal so,

•°•AB=BC=CD=AD=30m

and

•Diagonal BD=48m

•°•Area Of Rhombus = Area of ∆ABD+Area of ∆BDC

Finding the area of ∆ABD

Area of triangle =s√(s-a)(s-b)(s-c)

Here s is the semi perimeter,

and a,b and c are sides of the triangle ABD

a=30,b=30 nd c=48

s=a+b+c/2

s=30+30+48/2=54m

$area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{54(54 - 30)(54 - 30)(54 - 48)} \\ \\ = \sqrt{54(24)(24)6} \\ \\ = 6 \times 3 \times 24 \\ \\ = 432 {m}^{2}$

Hence area of ∆ABD=432m^2

Similarly area of ∆BDC=432m^2

so, Area of rhombus ABCD=Area of ∆ABD+Area of ∆BDC

=>Area of rhombus=(432+432)m^2=864m^2

Thus,

Area of rhombus =864m^2

Acc.to ques 18 cows will graze the field

so Area for 18 cows = Area of rhombus

Area for each cow = Area of rhombus/. 18=864/18=48m^2

Hence,

$<b><U><I>Each cow will get 48 m^2 Area for grazing</I></U></b>$

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Hope it helped uh !!

$\huge{\mathfrak{Thanks}}$

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