Question

 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 1

Hi friend,


When we will make a rhombus ABCD with a diagonal BD, we will get two triangles
triangle ABD
triangle BCD

Now , we will find the area od triangle ABD with Heron's Formula

s = a+b+c/2
= 30+30+48/2
= 108/2
= 54m

Area = √( s(s-a)(s-b)(s-c) )
= \√( 54 (54-30) (54+30) (54+48) )
= √( 54 * 24 * 24 * 6 )
= √ ( 2*3*3*3*2*2*2*3*2*2*2*3*2*3) (through prime factorization)
= √( 2*2*2*2*2*2*2*2*3*3*3*3*3*3)
= 432m2

Area of triangle BCD = 432*2
= 864m2

Area of grass field each cow will be getting = 864 / 18
= 48m2.

Hope I helped you a little!!!!

Answer 2

Diagonal AC divides the rhombus ABCD into two congruent triangles of equal area. 


Semi perimeter of ΔABC = (30 + 30 + 48)/2 m = 54 m
Using heron's formula,
Area of the ΔABC = √s (s-a) (s-b) (s-c)
                                       = √54(54 - 30) (54 - 30) (54 - 48) m2
                                       = √54 × 24 × 24 ×
6 cm2
                                       = 432 m2
Area of field = 2 × area of the ΔABC = (2 × 432)m2 = 864 m2
Thus,
Area of grass field which each cow will be getting = 864/18 m2 = 48 m2