Question

A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and it's longer diagonal is 48m how much area of the grass field will each cow be getting. ..

Answer 1

We know that the diagonals of the rhombus bisect each other at right angle .Using Pythagoras theorem ,I have..

________ _______

OD=√AD²-AO² =√30²-24²m

___________

=√【30+24)(30-24)m

______

√54×6m

_______

√9×6×6m

(3×6)m =18m

Area of one triangle AOD=(1/2×24×18)m^2

=216m^2

Area of rhombus =4×∆AOD

= (4×216(m^2=864m^2

Grass area for 18 cows =864m^2

Grass area for 1 cow=864/18=48m^2

OR

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 = root ( s(s-a)(s-b)(s-c) )
= root ( 54 (54-30) (54+30) (54+48) )
= root ( 54 * 24 * 24 * 6 )
= root ( 2*3*3*3*2*2*2*3*2*2*2*3*2*3) (through prime factorization)
= root ( 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