Question

12m
28.
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

Step-by-step explanation:

please mark it as brainliest ❤️

Answer 2

AnswEr :

48 m².

$\bf{\pink{\underline{\underline{\bf{Given\::}}}}}$

A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m. And it's longer diagonal is 48 m.

$\bf{\pink{\underline{\underline{\bf{To\:find\::}}}}}$

The area of grass field will each cow be getting.

$\bf{\pink{\underline{\underline{\bf{Explanation\::}}}}}$

We know that all sides are equal in rhombus.

We suppose a rhombus has ABCD is a rhombus.

$\bf{We\:have}\begin{cases}\sf{The\:18\:cows\:grazing\:in\:field}\\ \sf{Side\:of\:each\:rhombus\:(s)=30\:m}\\ \sf{Diagonal\:of\:rhombus\:(d)=48\:m}\end{cases}}$

$\bf{\red{\underline{\underline{\tt{A.T.Q\::}}}}}$

$\star\:\bf{\orange{\underline{\mathcal{USING\:HERONS\:FORMULA\::}}}}$

In Δ BCD :

• a = 30 m
• b = 30 m
• c = 48 m

$\leadsto\sf{Semi-perimeter=\dfrac{a+b+c}{2} }\\\\\\\leadsto\sf{Semi-perimeter=\dfrac{30+30+48}{2} m}\\\\\\\leadsto\sf{Semi-perimeter=\cancel{\dfrac{108}{2} }m}\\\\\\\leadsto\sf{\green{Semi-perimeter=54\:m}}$

$\bf{\underline{\underline{\tt{Area\:of\:triangle\::}}}}}$

$\leadsto\sf{Area_{\triangle}={\red{\sqrt{s(s-a)(s-b)(s-c)}} }}\\\\\leadsto\sf{Area_{\triangle}={\sqrt{54(54-30)(54-30)(54-48)} }}\\\\\leadsto\sf{Area_{\triangle}=\sqrt{54(24)(24)(6)}} \\\\\leadsto\sf{Area_{\triangle}=\sqrt{186624} }\\\\\leadsto\sf{\green{Area_{\triangle}=432\:m^{2} }}$

Now;

$\bf{\underline{\underline{\bf{Area\:of\:the\:field\::}}}}}$

$\leadsto\sf{Area_{field}=2\times \triangle BCD}}\\\\\leadsto\sf{Area_{field}=2\times 432\:m^{2} }\\\\\leadsto\sf{\green{Area_{field}=864\:m^{2} }}$

$\blacksquare\bf{\underline{\underline{\sf{Area\:of\:grass\:field\:will\:each\:cow\:be\:getting\::}}}}}$

$\mapsto\sf{18\:cows\times Each\:cow\:area=864\:m^{2} }\\\\\\\mapsto\sf{Each\:cow\:area=\dfrac{\cancel{864}\:m^{2} }{\cancel{18}}} \\\\\\\mapsto\sf{\green{Each\:cow\:area=48\:m^{2}}}$