Question

the perimeter of a rectangle is 64 meter and area is 207 meter square. find the length and the breath of the rectangle

Answer 1

DIAGRAM :

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GIVEN:

• Perimeter of rectangle - $\sf\:64m$
• Area of rectange - $\sf\: 207{m}^{2}$

TO FIND,

Length and breadth of rectangle.

LET,

• Length of rectangle be L.
• Breadth of rectangle be B.

$\boxed{\sf{\:Area\:of\:rectangle \:=\: length\times breadth}}$

$\boxed{\sf{\:Perimeter\:of\:rectange\:=\: 2\times(Length + breadth)}}$

$\underbrace{from\:first\:condition}$

$\longrightarrow\sf\: L \times B = 207 \\ \\ \longrightarrow\sf \: B = \frac{207}{L}................(1)$

$\underbrace{from\:second\:condition}$

$\longrightarrow\sf\: 2 \times (L + B)= 64 \\ \\ \longrightarrow \sf\:L + B = 32.............(2)$

Putting the value of B from (1) in (2)

$\longrightarrow \sf \: L + \frac{207}{L}=32 \\ \\ \longrightarrow \sf\: {L}^{2} + 207 = 32 Length$

$\longrightarrow \sf\: {L}^{2} - 32l + 207 = 0 \\ \\ \longrightarrow\sf\: {L}^{2} - 23L - 9L +207 = 0 \\ \\ \longrightarrow \sf\: L(L - 23) - 9(L - 23) = 0 \\ \\ \longrightarrow \sf\: (L - 23)(L - 9) = 0 \\ \\ \longrightarrow \sf\: L = 23\:or\:9$

$\sf {Now\:putting\:the\:value\:of\:L\:in\:(1)}$

$\sf{If\:we\:will\:take\:L\:=\:23\:then,}$

$\longrightarrow \sf\:B = \frac{207}{23}= 9m$

$\sf{If\:we\:will\:take\:L\:=\:9\:then,}$

$\longrightarrow \sf\:B = \frac{207}{9}= 23m$

$\overbrace{\underbrace{first\:condition}}$

$\boxed{\sf{Length = 23m}}$

$\boxed{\sf{Breadth = 9m}}$

$\overbrace{\underbrace{Second\:condition}}$

$\boxed{\sf{Length = 9m}}$

$\boxed{\sf{Breadth = 23m}}$

Answer 2

Answer:

DIAGRAM :

GIVEN:

Perimeter of rectangle - \sf\:64m64m

Area of rectange - \sf\: 207{m}^{2}207m

2

TO FIND,

Length and breadth of rectangle.

LET,

Length of rectangle be L.

Breadth of rectangle be B.

\boxed{\sf{\:Area\:of\:rectangle \:=\: length\times breadth}}

Areaofrectangle=length×breadth

\boxed{\sf{\:Perimeter\:of\:rectange\:=\: 2\times(Length + breadth)}}

Perimeterofrectange=2×(Length+breadth)

\underbrace{from\:first\:condition}

fromfirstcondition

\begin{lgathered}\longrightarrow\sf\: L \times B = 207 \\ \\ \longrightarrow\sf \: B = \frac{207}{L}................(1)\end{lgathered}

⟶L×B=207

⟶B=

L

207

................(1)

\underbrace{from\:second\:condition}

fromsecondcondition

\begin{lgathered}\longrightarrow\sf\: 2 \times (L + B)= 64 \\ \\ \longrightarrow \sf\:L + B = 32.............(2)\end{lgathered}

⟶2×(L+B)=64

⟶L+B=32.............(2)

Putting the value of B from (1) in (2)

\begin{lgathered}\longrightarrow \sf \: L + \frac{207}{L}=32 \\ \\ \longrightarrow \sf\: {L}^{2} + 207 = 32 Length\end{lgathered}

⟶L+

L

207

=32

⟶L

2

+207=32Length

\begin{lgathered}\longrightarrow \sf\: {L}^{2} - 32l + 207 = 0 \\ \\ \longrightarrow\sf\: {L}^{2} - 23L - 9L +207 = 0 \\ \\ \longrightarrow \sf\: L(L - 23) - 9(L - 23) = 0 \\ \\ \longrightarrow \sf\: (L - 23)(L - 9) = 0 \\ \\ \longrightarrow \sf\: L = 23\:or\:9\end{lgathered}

⟶L

2

−32l+207=0

⟶L

2

−23L−9L+207=0

⟶L(L−23)−9(L−23)=0

⟶(L−23)(L−9)=0

⟶L=23or9

\sf {Now\:putting\:the\:value\:of\:L\:in\:(1)}NowputtingthevalueofLin(1)

\sf{If\:we\:will\:take\:L\:=\:23\:then,}IfwewilltakeL=23then,

\longrightarrow \sf\:B = \frac{207}{23}= 9m⟶B=

23

207

=9m

\sf{If\:we\:will\:take\:L\:=\:9\:then,}IfwewilltakeL=9then,

\longrightarrow \sf\:B = \frac{207}{9}= 23m⟶B=

9

207

=23m

\overbrace{\underbrace{first\:condition}}

firstcondition

\boxed{\sf{Length = 23m}}

Length=23m

\boxed{\sf{Breadth = 9m}}

Breadth=9m

\overbrace{\underbrace{Second\:condition}}

Secondcondition

\boxed{\sf{Length = 9m}}

Length=9m

\boxed{\sf{Breadth = 23m}}

Breadth=23m