A rhombus shaped field has green grass for 15 cows. If each side of the rhombus is 200 m and its one of the
diagonals is 320 m, then find the area of the grass field that will be grazed by each cow.
Answers
Answer:
A rhombus shaped field has green grass for 18 cows
One side of the rhombus = 30 m
Diagonal = 48 cm
In Δ ABC
a = 48cm
b = 30cm
c = 30cm
As the semi-perimeter is the half of the sum of sides of the triangle.
s = \frac{a + b + c}{2}
2
a+b+c
s = \frac{48 + 30 + 30}{2}
2
48+30+30
s = \frac{108}{2}
2
108
s = 54m.
Therefore area of triangle =
\begin{gathered} = \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \: \sqrt{54(54 - 48)(54 - 30)(54 - 30} \\ \\ = \: \sqrt{54 \times 6 \times 24 \times 24} \\ \\ = \: \sqrt{3 \times 3 \times 6 \times 6 \times 24 \times 24} \\ \\ = \: 3 \times 6 \times {24}^{2} \\ \\ = \: 18 \times {24}^{2} \\ \\ = \: {432m}^{2} \end{gathered}
=
s(s−a)(s−b)(s−c)
=
54(54−48)(54−30)(54−30
=
54×6×24×24
=
3×3×6×6×24×24
=3×6×24
2
=18×24
2
=432m
2
Therefore area of rhombus = 2 \times 4322×432 = {864}^{2}864
2
Therefore are of the grass for 18 cows = {864}^{2}864
2
Therefore area of the grass for one cow = \frac{864}{18}
18
864
Answer = {48m}^{2}48m
2
Answer:
Step-by-step explanation:
