Question

The length of a rectangular hall is 3 metres more than double of its breadth. If its perimeter is
60 metres, what is its length?​

Answer 1

✬ Length = 21 m ✬

Step-by-step explanation:

Given:

• Length of rectangular hall is 3 metre more than double its breadth.
• Perimeter of a rectangular hall is 60 m.

To Find:

• What is its length ?

Solution: Let breadth be x . Therefore

➟ Double of breadth = 2x

➟ Length = 3 m more than 2x

➟ Length = (2x + 3)

As we know that

★ Perimeter of Rectangle = 2(Length + Breadth) ★

A/q

• Perimeter is 60 m.

$\implies{\rm }$ 60 = 2(2x + 3 + x)

$\implies{\rm }$ 60 = 2(3x + 3)

$\implies{\rm }$ 60 = 6x + 6

$\implies{\rm }$ 60 – 6 = 6x

$\implies{\rm }$ 54 = 6x

$\implies{\rm }$ 54/6 = x

$\implies{\rm }$ 9 = x

So, measure of

• Breadth is x = 9 m
• Length is 2x + 3 = 2(9) + 3 = 21 m

[ Verification ]

• 60 = 2(21 + 9)
• 60 = 60

$\large\bold{\texttt {Verified }}$

Answer 2

Given:

• Length of the Rectangle hall is 3m more than it's Breadth.

• Perimeter of Rectangle = 60m

Find:

• Length of the Rectangle

Solution:

$\sf \star \red{Let, \: breadth \: of \: hall = xm}$

$\sf \star \blue{so, \: length \: of \: hall = 2x + 3m}$

We, know that

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

where,

• Perimeter of Rectangle = 60m
• Length of Rectangle = 2x + 3m
• Breadth of Rectangle = x m

So,

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

$\sf \implies \pink{ 60= 2(2x + 3+ x)}$

$\sf \implies \pink{ 60= 2(3x + 3)}$

$\sf \implies \pink{ 60= 6x + 6}$

$\sf \implies \pink{ 60 - 6= 6x}$

$\sf \implies \pink{ 54= 6}$

$\sf \implies \pink{x = \cancel{\dfrac{54}{6}}= 9m}$

$\sf \implies \pink{x = 9m}$

$\underline{\footnotesize{\sf So, length \: of \: rectangle = 2x + 3 = 2(9) + 3= 18 + 3 = 21m}}$

$\underline{\footnotesize{\sf and \: breadth \: of \: rectangle = x = 9m}}$

_________________

Verification

Perimeter of Rectangle = 2(l+b)

$\to \orange{\sf 2(21+9) = 60}$

$\to \orange{\sf 2(30) = 60}$

$\to \orange{\sf 60 = 60}$

L.H.S = R.H.S

Hence, Verified