Question

The length of a rectangle is 5 metres less than twice the breadth. If the perimeter is 50metres, find the length and breadth of the rectangle.​

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Understanding \: the \: question...}}}}}$

⋆ This question says that we have to find out the length and breadth of the rectangle when the length of a rectangle is 5 metres less than twice the breadth. It is also provided that the perimeter of the given rectangle is 50 metres. Now let us solve this question!

${\bigstar \:{\pmb{\sf{\underline{Figure...}}}}}$

⋆ The figure is related to the simple structure of a rectangle:

$\begin{gathered} \sf Length \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \sf Breadth\end{gathered}$

⠀⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━

${\bigstar \:{\pmb{\sf{\underline{Given \: that...}}}}}$

⋆ The length of a rectangle is 5 metres less than twice the breadth.

⋆ The perimeter is 50 metres.

${\bigstar \:{\pmb{\sf{\underline{To \: find...}}}}}$

⋆ Length of the rectangle

⋆ Breadth of the rectangle

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ Length of the rectangle = 15 m

⋆ Breadth of the rectangle = 10 m

${\bigstar \:{\pmb{\sf{\underline{Using \: concept...}}}}}$

⋆ Formula to find perimeter of rectangle

${\bigstar \:{\pmb{\sf{\underline{Using \: formula...}}}}}$

${\small{\underline{\boxed{\sf{\star \: Perimeter \: of \: rectangle \: = 2(l+b)}}}}}$

⠀⠀⠀⠀⠀⠀(Where, l denotes length and b denotes breadth)

${\bigstar \:{\pmb{\sf{\underline{Full \; Solution...}}}}}$

$\qquad \qquad \qquad{\pmb{\sf{Case \: 1^{st}}}}$

~ As it is provided to us that the length of a rectangle is 5 metres less than twice the breadth henceforth,

⇒ Length = (2b - 5) metres

⇒ Breadth = ?

⇒ Perimeter = 50 metres

~ Now as we get the conditional length of the rectangle and breadth be b itself, perimeter is also provided. So let us use the formula to find perimeter of rectangle to find it's breadth first.

⇒ Perimeter of rectangle = 2(l+b)

⇒ 50 = 2(2b-5+b)

⇒ 50 = 2(3b-5)

⇒ 50 = 6b - 10

⇒ 50 + 10 = 6b

⇒ 60 = 6b

⇒ 60/6 = b

⇒ 10 = b

⇒ b = 10 metres

⇒ Breadth = 10 metres

$\qquad \qquad \qquad{\pmb{\sf{Case \: 2^{nd}}}}$

~ Now as we get the breadth, so now let us imply 10 as b in conditional length.

⇒ Length = (2b - 5) metres

⇒ Length = 2(10) - 5

⇒ Length = 20 - 5

⇒ Length = 15 metres

• Length = 15 metres
• Breadth = 10 metres

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${\bigstar \:{\pmb{\sf{\underline{Verification...}}}}}$

~ Now let us veriy the solution that we do this question correctly or not. To verify the result we just have to use perimeter of rectangle formula and have to put the values that we get of length and breadth.

⇒ Perimeter of rectangle = 2(l+b)

⇒ 50 = 2(15+10)

⇒ 50 = 2(25)

⇒ 50 = 50

⇒ LHS = RHS

Henceforth, verified!!

Answer 2

Answer:

$Given:−</p><p> </p><p> </p><p> </p><p> †</p><p></p><p>Given:−</p><p></p><p>The length of a rectangle is 5 metres less than twice the breadth. Perimeter of the rectangle is 50 m.</p><p></p><p>\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}† </p><p>ToFind:−</p><p> </p><p> </p><p> </p><p> </p><p></p><p>†</p><p></p><p>Length and Breadth of the rectangle</p><p></p><p>\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}† </p><p>Solution:−</p><p> </p><p> </p><p> </p><p> </p><p></p><p>First,</p><p></p><p>Let</p><p></p><p>Breadth be b</p><p></p><p>Length be l</p><p></p><p>According to the question,</p><p></p><p>Breadth = b</p><p></p><p>Length is 5 meters less than twice the breadth.</p><p></p><p>This implies that,</p><p></p><p>Length = 2b - 5</p><p></p><p>And</p><p></p><p>Perimeter of the rectangle is 50 m.</p><p></p><p>We know that,</p><p></p><p>\boxed{\pink{\sf Perimeter \: of \: rectangle \: = \: 2 \: (l \: + \: b)}} </p><p>Perimeterofrectangle=2(l+b)</p><p> </p><p> </p><p></p><p>Here,</p><p></p><p>l = 2b - 5</p><p></p><p>b = b</p><p></p><p>Perimeter of Rectangle = 50</p><p></p><p>Substituting the values,</p><p></p><p>\sf 50 \: = \: 2 \: (2b \: - \: 5 \: + \: b) 50=2(2b−5+b)</p><p></p><p>\sf 50 \: = \: 2 \: (3b \: - \: 5) 50=2(3b−5)</p><p></p><p>\sf 50\: = \: 6b \: - \: 10 50=6b−10</p><p></p><p>\sf 50 \: + \: 10 \: = \: 6b 50+10=6b</p><p></p><p>\sf 60 \: = \: 6b 60=6b</p><p></p><p>\sf b \: = \: \dfrac{60}{6} b=</p><p></p><p>6</p><p></p><p>60</p><p></p><p>Breadth of the rectangle = 15m and 10m.}}}} ∙⇝</p><p></p><p>Length and Breadth of the rectangle = 15m and 10m.</p><p></p><p>\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Formulas \: Used:-}}}}}}}† </p><p>FormulasUsed:−</p><p> </p><p> </p><p> </p><p> </p><p></p><p>†</p><p></p><p>FormulasUsed:−</p><p></p><p>< /p > < p > \sf Perimeter \: of \: rectangle \: = \: 2 \: (l \: + \: b) Perimeterofrectangle=2(l+b) < /p > < p > < /p > < p > where,</p><p>Perimeterofrectangle=2(l+b)Perimeterofrectangle=2(l+b)</p><p></p><p>where,</p><p></p><p>l is length of the rectangle</p><p></p><p>b is the breadth of the rectangle$

Step-by-step explanation:

Given:−

†

Given:−

The length of a rectangle is 5 metres less than twice the breadth. Perimeter of the rectangle is 50 m.

\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}†

ToFind:−

†

Length and Breadth of the rectangle

\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}†

Solution:−

First,

Let

Breadth be b

Length be l

According to the question,

Breadth = b

Length is 5 meters less than twice the breadth.

This implies that,

Length = 2b - 5

And

Perimeter of the rectangle is 50 m.

We know that,

\boxed{\pink{\sf Perimeter \: of \: rectangle \: = \: 2 \: (l \: + \: b)}}

Perimeterofrectangle=2(l+b)

Here,

l = 2b - 5

b = b

Perimeter of Rectangle = 50

Substituting the values,

\sf 50 \: = \: 2 \: (2b \: - \: 5 \: + \: b) 50=2(2b−5+b)

\sf 50 \: = \: 2 \: (3b \: - \: 5) 50=2(3b−5)

\sf 50\: = \: 6b \: - \: 10 50=6b−10

\sf 50 \: + \: 10 \: = \: 6b 50+10=6b

\sf 60 \: = \: 6b 60=6b

\sf b \: = \: \dfrac{60}{6} b=

6

60

Breadth of the rectangle = 15m and 10m.}}}} ∙⇝

Length and Breadth of the rectangle = 15m and 10m.

\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Formulas \: Used:-}}}}}}}†

FormulasUsed:−

†

FormulasUsed:−

< /p > < p > \sf Perimeter \: of \: rectangle \: = \: 2 \: (l \: + \: b) Perimeterofrectangle=2(l+b) < /p > < p > < /p > < p > where,</p><p>Perimeterofrectangle=2(l+b)Perimeterofrectangle=2(l+b)</p><p></p><p>where,

l is length of the rectangle

b is the breadth of the rectangle