Question

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

Answer 1

Answer:

Appropriate Question :-

• The length of a rectangle is 5 m less than twice the breadth, if the perimeter is 50 m. Find the length and breadth of the rectangle.

Given :-

• The length of a rectangle is 5 m less than twice the breadth, if the perimeter is 50 m.

To Find :-

• What is the length and breadth of the rectangle.

Formula Used :-

$\clubsuit$ Perimeter of Rectangle Formula :

$\longmapsto \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}$

Solution :-

Let,

$\mapsto$ Breadth = b m

$\mapsto$ Length = 2b - 5 m

Given :

$\bigstar$ Perimeter = 50 m

According to the question by using the formula we get,

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

$\implies \sf 4b - 10 + 2b =\: 50$

$\implies \sf 4b + 2b - 10 =\: 50$

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

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

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

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

$\implies \sf b =\: \dfrac{10}{1}$

$\implies \sf\bold{\purple{b =\: 10\: m}}$

Hence, the required length and breadth are :

$\dashrightarrow$ Length of Rectangle :

$\longrightarrow \sf 2b - 5\: m$

$\longrightarrow \sf 2(10) - 5\: m$

$\longrightarrow \sf 20 - 5\: m$

$\longrightarrow \sf\bold{\red{15\: m}}$

And,

$\dashrightarrow$ Breadth of Rectangle :

$\longrightarrow \sf b\: m$

$\longrightarrow \sf\bold{\red{10\: m}}$

$\therefore$ The length and breadth of a rectangle is 15 m and 10 m respectively.

Answer 2

$\bf\red{Given:-}$

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

$\bf\red{To \: Find:-}$

• Length and Breadth of the rectangle

$\bf\red{Solution:-}$

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

• Perimeter of the rectangle is 50 m.

We know that,

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

Here,

• l = 2b - 5

• b = b

• Perimeter of the rectangle = 50.

Substituting the values,

• 50 = 2 ( 2b - b + 5 )

• 50 = 2 ( 3b - 5 )

• 50 = 6b - 10

• 50 + 10 = 6b

• 60 = 6b

• $b = \frac{60}{6}$

• b = 10 m

Then,

• l = 2b - 5

Substituting the value,

• = 2 * 10 - 5

• l = 20 - 5

• l = 15 m

Therefore,

• Length = 10 m

• Breadth = 15m