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:
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 =
= 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 = 24322×432 = {864}^{2}864
2
Therefore are of the grass for 18 cows = {864}^{2}864
2
Therefore area of the grass for one cow = {864}{18}
18
864
Answer = {48m}^{2}48m
2
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