Question

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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 1

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Refer the attachment for my answer.

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Answer 2

Answer:

48m square

Step-by-step explanation:

Let the longer diagonal AC divides the rhombus ABCD into two congruent triangles.

For ∆ABC, a = b = 30 m, c = 48 m

And Semi Perimeter(s) = (a + b + c)/2

s = (30 + 30 + 48)/2

s = 108/2

s = 54 m

By using Heron’s formula,

Area of ΔABC = √s(s - a)(s - b)(s - c)

= √54(54 - 30)(54 - 30)(54 - 48)

= √54 × 24 × 24 × 6

Area of ΔABC = 432 m2

Area of rhombus = 2 × Area of a ΔABC

= 2 × 432 m2

= 864 m2

Since, number of cows = 18

The area of grass field will each cow get = (Total area of the rhombus) / 18

= 864 m2/18

= 48 m2

Thus, each cow will be getting a 48 m2 area of the grass field.