Question

A triangular shaped field has green grass for 18 cows to graze. The
two sides are 30m and 48m and the perimeter is 108m, how much area
of grass field will each cow be getting ?

Answer 1

Step-by-step explanation:

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= a+b+c/2

=30+30+48/2

=108/2

=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

Hence Area of △ABD=432m

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

Area of △BCD=432 m

So, Area of rhombus ABCD

= Area of △ABD + Area △BCD

=432+432

=864m

Thus, Area of Rhombus=864m

Given that 18 cows to graze the field.

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

Area of Each cow= Area of rhombus/18

=864/18

=48m

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

Answer 2

Answer:

24 meter square area of grass is available for each cow

Step-by-step explanation:

perimeter (p) = 108 m

side (a) = 30 m

side (b) = 48 m

∴ side (c) = p - ( a+b )

               = 108 - ( 30+48 )

               = 30 m

Now ,

        ∵ semi-perimeter (s) = perimeter (p) ÷ 2

         ∴ s = 54 m

total area Δ = √ [ s ( s - a ) ( s - b ) ( s - c ) ]

                  = √ [ 54 ( 54 - 30 ) ( 54 - 48 ) ( 54 - 30 ) ]

                  = √ [ 54 × 24 × 6 × 24 ]

                  = 24 × 6 × 3

                  = 432 m²

Hence total area of grass land available for each cow is = 432 ÷ 18

                                                                                      = 24 m²