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

Here are your answers. Hope they help!

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