Question

A rectangular field measuring 30m by 25m is divided in two identical square plot

of a land find the largest possible length of a side of each square plot of a land.

​

Answer 1

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$\sf \underbrace{Let's \: understand \: concept \: 1'st}$

$\sf \small\text{Here the Concept of Area of square and Area of} \\ \sf \small \text{ rectangle has been used . According to this , it \: \: } \\ \sf \small \text{ given that the rectangular field has been divided } \\ \sf \small \text{into two square plots Then the sum of area of two } \\ \sf \small \ \text{equal \: square plots. will be equal to the the area of } \\ \sf \small \text{whole field rectangular field using this concept ,} \\ \bf\small \text \green{ Let's do it !!}$

$\sf \large{ \frac{ \star \: fσrmulα \: uѕєd \star}{──────────}}$

$\sf \small{ \mapsto \: Area \: of \: Rectangle \: = Length \: ( L ) × \: Breadth \: ( B )}$

$\sf \small{ \mapsto \: Area \: of \: square \: = (side )^{2} }$

$\sf \large{ \frac{ \star \: Quєѕtíσn \: \star}{──────────}}$

$\sf \small \text{A rectangular field measuring 30m by 25m is divided} \\ \sf \small \text{ in two identical square plot of a land find the \: largest } \\ \sf \small \text { possible length of a side of each square plot of a land. \: }$

$\sf \large{ \frac{ \star \: Sσlutíσn \: \star}{──────────}}$

$\sf \small \text \red{Given, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small \text{⇛Dimension of Rectangle plot = 30 m × 25 m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \: \: \: \: } \\ \sf \small \text{⇛Number of identical square in which the rectangular plot has been divided = 2}$

$\sf \small \text{It is given that , the land has been divided into two identical square. Then,the } \\ \sf \small \text{ Area of these square will be equal thus the side of these square also must be equal.} \\ \sf \small \text{Then, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small \text{Let the side of each square be \bf{'x' m } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small \text{Then, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\sf \small \text{Area according to the the concept, We get } \\ \sf \small { \implies \: x^{2} + x^{2} = 30 \times 25 } \\ \sf \small \text{Since area of both square is equal. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small{ \implies \: 2x^{2} = 750 \: sq.m \: \: \: \: \: } \\ \sf \small{ \implies \: x^{2} = \frac{ \cancel{750}}{ \cancel{2}} = 375 \: sq.m } \\ \sf \small{ \mapsto \: x ^{2} = 375 } \\ \sf \small \red{ \mapsto \: x = \sqrt{375} = 19.364916731}$

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$\sf \small \text{Hence the largest of each side of square = \bf \red{ x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small \text{Hence the largest possible length of the side \: of \: each \: square \: plot \: is \: = \bf \red{19.364916731}}$

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Answer 2

Answer:

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\sf \underbrace{Let's \: understand \: concept \: 1'st}

Let

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st

\begin{gathered}\sf \small\text{Here the Concept of Area of square and Area of} \\ \sf \small \text{ rectangle has been used . According to this , it \: \: } \\ \sf \small \text{ given that the rectangular field has been divided } \\ \sf \small \text{into two square plots Then the sum of area of two } \\ \sf \small \ \text{equal \: square plots. will be equal to the the area of } \\ \sf \small \text{whole field rectangular field using this concept ,} \\ \bf\small \text \green{ Let's do it !!}\end{gathered}

Here the Concept of Area of square and Area of

rectangle has been used . According to this , it

given that the rectangular field has been divided

into two square plots Then the sum of area of two

equal square plots. will be equal to the the area of

whole field rectangular field using this concept ,

Let’s do it !!

\sf \large{ \frac{ \star \: fσrmulα \: uѕєd \star}{──────────}}

──────────

⋆fσrmulαuѕєd⋆

\sf \small{ \mapsto \: Area \: of \: Rectangle \: = Length \: ( L ) × \: Breadth \: ( B )}↦AreaofRectangle=Length(L)×Breadth(B)

\sf \small{ \mapsto \: Area \: of \: square \: = (side )^{2} }↦Areaofsquare=(side)

2

\sf \large{ \frac{ \star \: Quєѕtíσn \: \star}{──────────}}

──────────

⋆Quєѕt

ı

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\begin{gathered} \sf \small \text{A rectangular field measuring 30m by 25m is divided} \\ \sf \small \text{ in two identical square plot of a land find the \: largest } \\ \sf \small \text { possible length of a side of each square plot of a land. \: }\end{gathered}

A rectangular field measuring 30m by 25m is divided

in two identical square plot of a land find the largest

possible length of a side of each square plot of a land.

\sf \large{ \frac{ \star \: Sσlutíσn \: \star}{──────────}}

──────────

⋆Sσlut

ı

ˊ

σn⋆

\begin{gathered} \sf \small \text \red{Given, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small \text{⇛Dimension of Rectangle plot = 30 m × 25 m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \: \: \: \: } \\ \sf \small \text{⇛Number of identical square in which the rectangular plot has been divided = 2}\end{gathered}

Given, :

⇛Dimension of Rectangle plot = 30 m × 25 m : :

⇛Number of identical square in which the rectangular plot has been divided = 2

\begin{gathered} \sf \small \text{It is given that , the land has been divided into two identical square. Then,the } \\ \sf \small \text{ Area of these square will be equal thus the side of these square also must be equal.} \\ \sf \small \text{Then, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small \text{Let the side of each square be \bf{'x' m } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small \text{Then, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }\end{gathered}

It is given that , the land has been divided into two identical square. Then,the

Area of these square will be equal thus the side of these square also must be equal.

Then,

Let the side of each square be ’x’ m

Then,

\begin{gathered} \sf \small \text{Area according to the the concept, We get } \\ \sf \small { \implies \: x^{2} + x^{2} = 30 \times 25 } \\ \sf \small \text{Since area of both square is equal. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \small{ \implies \: 2x^{2} = 750 \: sq.m \: \: \: \: \: } \\ \sf \small{ \implies \: x^{2} = \frac{ \cancel{750}}{ \cancel{2}} = 375 \: sq.m } \\ \sf \small{ \mapsto \: x ^{2} = 375 } \\ \sf \small \red{ \mapsto \: x = \sqrt{375} = 19.364916731}\end{gathered}

Area according to the the concept, We get

⟹x

2

+x

2

=30×25

Since area of both square is equal.

⟹2x

2

=750sq.m

⟹x

2

=

2

750

=375sq.m

↦x

2

=375

↦x=

375

=19.364916731