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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?

Answer :

Let ABCD be a rhombus.

Area of the rhombus ABCD
= 2 × area of $$\triangle{ABD}$$ ... (i)

As we know that, in a rhombus, diagonals divides it in two equal parts.

In $$\triangle{ABD}$$, we have,
AB = 30 m, BD = 48 m, DA=30 m

Now, we know that,

$$s = \frac{AB + BD + AD}{2}$$
$$\therefore$$ $$s = \frac{30 + 48 + 30}{2} = \frac{108}{2} = 54m$$

Now, Area of triangle
= $$\sqrt{54(54 - 30)(54 - 48)(54 - 30)}$$
(Since, Heron's formula [area = $$\sqrt{s(s - a)(s - b)(s - c)}$$])

= $$\sqrt{54 × 24 × 6 × 24}$$
= $$\sqrt{9 × 6 × 4 × 6 × 6 × 4 × 6}$$
= $$3 × 6 × 6 × 4 {m}^2$$
= $$432 {m}^2$$

Thus, from Equation (i),

Area of rhombus
= 2 × 432m
= 864 m

Also, Number of cows = 18

So, therefore, Area of grass field per cow
= $$\frac{864}{18}$$ = $$48 {m}^2$$.