Question

the length of a rectangle is 5 meters less than twice the breath. if perimeter is 50 meters find length and breadth algebra​

Answer 1

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

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