Question

Arhombus 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,
what is the area of the field?​

Answer 1

Answer:

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Step-by-step explanation:

Let ABCD is a rhombus and length of each side is 30

Length of diagonal AC is 48

From Δ ABC,

Let AB =a =30

AC = b =48

BC = c = 30

Now s = (a+b+c)/2

=> s = (30+48+30)/2

=> s = 108/2

=> s = 54 m

Now area of Δ ABC = √{s*(s-a)*(s-b)*(s-c)}

= √{54*(54-30)*(54-48)*(54-30)}

= √{54*24*6*24}

= √{9*6*24*6*24}

= 3*6*24

= 432 m2

Area of rhombus ABCD = 2*  area of Δ ABC (since area of Δ ABC = area of Δ ACD)

= 2* 432

= 864 m2

Now area of grash for 18 cows = 864 m2

So area of grash for 1 cows = 864/18 m2 = 48 m2