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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:

Draw a rhombus-shaped field first with the vertices as ABCD. The diagonal AC divides the

rhombus into two congruent triangles which are having equal areas. The diagram is as follows.

Consider the triangle BCD,

Its semi-perimeter = (48 + 30 + 30)/2 m = 54 m

Using Heron's formula,

Area of the ΔBCD =

\begin{aligned} &\sqrt{s(s-a)(s-b)(s-c)}\\ &(\sqrt{54(54-48)(54-30)(54-30)}) m^{2}\\ &\left.=432 \mathrm{m}^{2} \times 6 \times 24 \times 24\right) \mathrm{m}^{2}\\ &\text { Area of field }=2 \times \text { area of the } \Delta B C D=(2 \times 432) \mathrm{m}^{2}=864 \mathrm{m}^{2} \end{aligned}

Thus, the area of the grass field that each cow will be getting = (864 / 18) \mathrm{m}^{2}=48 \mathrm{m}^{2}

"hello students welcome to leader q a
video session i am saf your max tutor
and question for today is a rhombus
shaped field has
green grass for 18 cows to graze
if each side of the rhombus is 30 meter
and its longer diagonal is 48 meter
how much area of grass field will each
cow be getting
so first of all you draw the rhombus
shape field with the vertices
as shown in the figure so this rhombus
abcd is a
field as per the question
and you can see inside this rhombus
diagonal ac is there
which divides the rhombus into two
congruent triangles
and these triangles are triangle adb
and triangle bdc
or bcd
now consider triangle bcd inside this
triangle
first of all let us find semi parameter
to find its area
so s will be equal to 48
sum all the side and then divided by 2
so s will be equal to 54 meter
now use the harrows formula to find the
area so as per the harrows formula you
know
let it indicate as a that is area of the
triangle
so area will be equal to under root of
s s minus a s minus
b as minus c
let us substitute value of a b c and s
so this will give you
as is 54 54
minus 48
and then 54 minus 30
and then 54 minus 30 again
so this is our arrows formula applied we
will continue over here
so area comes out to be a is equal to
432 meter square
and hence area of the field will be 2
into
area of triangle bcd
because this field is made up of two
triangles
which are congruent as these two
triangles are congruent their area will
also be same
so you can say that this area of
triangle
abd will be equal to area of triangle
bcd
so you can see here that
the area of the field will be equal to 2
into area of
triangle bc d that is 2
into 432
the area will be equal to 864 meter
square
thus the area of the grass filled at
each
cow that each cow will be great grazing
will be equal to
864 meter square
divided by 18 as you can see there are
18 cows
we have to divide it by 18 for finding
the area grazed by each cow
864 divided by 18
and that comes out to be 48
square and that is our final answer
for the area area of the grass grazed by
each cow if you have any query you can
post it in our comment section
and subscribe to lido for more such q
and a thank you for watching
"

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