Question

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

Question:-

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

Given:-

↝Side of rhombus = 30m

↝Diagonal = 48 m

To find:-

Area of grass field each cow will get.

Solution:-

Area of rhombus = Area of ∆ᴀʙᴅ + ∆ ʙᴄᴅ

Finding the area of ∆ABD

Area of triangle =√s(s-a)(s-b)(s-c)

Here,

• a=30 m
• b=30 cm
• c=48 cm.

s=a+b+c/2

$=\frac{30+30+48}{2}$

$=\frac{108}{2}=54 m$

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

Putting a= 30m , b= 30m ,c=48m.

$=\sqrt{54(54-30)(54-30)(54-48)}$

$=\sqrt{54(24)(24)(6)}$

$=\sqrt{(6²)×(3²)×(24²)}$

=6×3×24

=432 m².

Hence area of ∆ᴀʙᴅ = 432m².

Similarly,

Area of ∆ʙᴄᴅ = 432m² ( as both have same sides)

So ,area of rhombus ABCD =Area of ∆ᴀʙᴅ +area of ∆ʙᴄᴅ

=432 m +432 m

=864 m².

Thus, Area of rhombus = 864 m²

Given that 18 cows to graze the field .

So, area for 18 cows = area of rhombus

Area if each cow =$\frac{area \:of \:rhombus}{18}$

=864/18

=48m².

Thus, each cow will get 48 m² area of grass field.

Answer 2

Answer:

Let ABCD be a rhombus of side 30m

AB=BC=CD=DA=30m

Also, diagonal=48m

BD=48m

Area of rhmbus=Area△ABD+Area△BCD

For △ABD,

Area of triangle=

s(s−a)(s−b)(s−c)

Here,s is the semi perimeter, and a,b,c are the sides of the triangle.

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

S=

2

a+b+c

=

2

30+30+48

=

2

108

=54m

Area of △ABD=

s(s−a)(s−b)(s−c)

Here a=30m,b=30m ,c=48m and s=54,

=

54(54−30)(54−30)(54−48)

=

54×24×24×6

=432m

2

Hence Area of △ABD=432m

2

As both △ABD and △BCD have the same sides,

Area of △BCD=432 m

2

So, Area of rhombus ABCD

= Area of △ABD + Area of △BCD=432+432=864m

2

Thus, Area of Rhombus=864m

2

Given that 18 cows to graze the field.

So, Area of 18 cows=Area of the rhombus.

Area of Each cow=

18

Areaofrhombus

=

18

864

=48m

2

Thus, each cow will get 48m

2

area of the grass field