Question

a field is in the shape of rhombus having each side 30m, its longer diagonal is 48m. In the field 18 cows are grazing and find how much area of grass each cow will have​

Answer 1

${\large{\bf{\red{\underline{\underline{Given :}}}}}}$

Side of Rhombus = 30m

Diagonal 1 = 48m

No. of cows who can graze the field = 18

${\large{\bf{\blue{\underline{\underline{To Find :}}}}}}$

• Find how much grass will each cow graze.

${\large{\bf{\orange{\underline{\underline{Solution :}}}}}}$

Now,

Sides :

• 1st side = 30m
• 2nd side = 30m
• 3rd side = 48m

After applying the diagonal the Rhombus will be devided into 2 triangles:

First,

${\blue{\boxed{\pink{\bf{S = \frac{a + b + c}{2} }}}}}$

${\mapsto{\bf{ \frac{30 + 30 + 48}{2} }}}$

${\mapsto{\bf{ {\cancel\frac{108}{2} }}}}$

${\red{\mapsto{\boxed{\sf{54 {m}^{2} }}}}}$

Than,

${\blue{\boxed{\pink{\bf{ area = \sqrt{s(s - a)(s - b)(s - c)} }}}}}$

${\mapsto{\bf{ \sqrt{54(54 - 30)(54 - 30)(48 - 30)} }}}$

${\mapsto{\bf{ \sqrt{54 \times 24 \times 24 \times 18} }}}$

${\red{\mapsto{\boxed{\sf{432 {m}^{2} }}}}}$

Next,

${\mapsto{\bf{Area \: of \: Rhombus = 2 × 432 {m}^{2} }}}$

${\red{\mapsto{\boxed{\sf{864 {m}^{2} }}}}}$

So,

${\sf{\purple{No. \: of \: cows = 18}}}$

${\sf{\purple{Total \: area \: of \: grass \: in \: field = 864 {m}^{2} }}}$

${\sf{\purple{1 \: cow \: will \: graze = {\cancel \frac{864}{18} }}}}$

${\blue{\dashrightarrow{\red{\boxed{\bf{48 {m}^{2} }}}}}}$

So,

${\tt{\blue{Each \: cow \: will \: graze \: 48 {m}^{2} .}}}$

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