Question

A rhombus shaped field has green grass for 36 cows to graze. If each side of the field is 30m and longer diagonal is 48m, then how much area of grass each cow will get if $216m^2$ of the area is not to be grazed.(Assume each cow grazes same amount)

• A. $6m^2$
• B. $12m^2$
• C. $18m^2$
• D. $29m^2$

Answer 1

The correct option is C $18m^2$

Let ABCD be the given rhombus shaped field.

In $\Delta AOB$, $OA=\sqrt{(30{)}^2-(24{)}^2}$
$=\sqrt{324}=18$
$\therefore$ Length of diagonal AC = 2(18)
= 36 m
Area of the field $=\frac{1}{2}\times 48\times 36m^2$
$=864m^2$
Area to be grazed by 36 cows
$=(864-216)m^2$
$=648m^2$
Area will be grazed by each cow = $\frac{648}{36}{m}^2$
$=18m^2$