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

Let $ABCD$ be a rhombus of side $30$m

$AB=BC=CD=DA=30$m

Also, diagonal$=48$m

$BD=48$m

Area of rhmbus$=$Area$△ABD+$Area$△BCD$

For $△ABD,$

Area of triangle$=\sqrt{s(s-a)(s-b)(s-c)}$

Here,$s$ is the semi perimeter, and $a,b,c$ are the sides of the triangle.

Here $a=30$m,$b=30$m and $c=48$m

$S=\frac{a+b+c}{2}=\frac{30+30+48}{2}=\frac{108}{2}=54$m

Area of $△ABD=\sqrt{s(s-a)(s-b)(s-c)}$

Here $a=30$m,$b=30$m ,$c=48$m and $s=54$,

$=\sqrt{54(54-30)(54-30)(54-48)}=\sqrt{54\times 24\times 24\times 6}=432m^2$

Hence Area of $△ABD=432m^2$

As both $△ABD$ and $△BCD$ have the same sides,

Area of $△BCD=432m^2$

So, Area of rhombus $ABCD$

= Area of $△ABD+$ Area of $△BCD=432+432=864m^2$

Thus, Area of Rhombus$=864m^2$

Given that $18$ cows to graze the field.

So, Area of $18$ cows$=$Area of the rhombus.

Area of Each cow$=\frac{Areaofrhombus}{18}=\frac{864}{18}=48m^2$

Thus, each cow will get $48m^2$ area of the grass field.