Question

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

Answer 1

Step-by-step explanation:

Let the breadth of the rectangle be x meter.

The length of a rectangle is 5 meters less than twice the breadth. So, twice the breadth is 2*x = 2x, and 5 meters less than twice the breadth is 2x-5.

Therefore, the length of the rectangle = (2x-5)m

Formula for perimeter of a rectangle = 2(l + b)

Perimeter of the rectangle = 50m = 2(l +b)

Therefore,

2(l + b) = 2(2x-5 + x)     {Substituting the values of l and b}

=50 = 2(3x-5) = 6x-10

=6x = 50 + 10 = 60

=x = 60/6 = 10m

Therefore,

Breadth = x = 10m

Length = 2x-5 = 2*10-5 = 20-5 = 15m

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Answer 2

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

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

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

Length and Breadth of the rectangle

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

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,

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

Here,

l = 2b - 5

b = b

Perimeter of Rectangle = 50

Substituting the values,

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

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

$\sf 50\: = \: 6b \: - \: 10$

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

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

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

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

b = 10 m

Then,

l = 2b - 5

Substituting the value,

l = 2 * 10 - 5

l = 20 - 5

l = 15 m

Therefore,

$\bullet{\leadsto} \: \underline{\boxed{\purple{\texttt{Length and Breadth of the rectangle = 15m and 10m.}}}}∙$

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

$\sf Perimeter \: of \: rectangle \: = \: 2 \: (l \: + \: b)$

• where,

l is length of the rectangle

b is the breadth of the rectangle