Question

The length of a rectangular hall is 9 metres more than its breadth.If the perimeter of the
hall is110m, find its:
(a) length (b) breadth

Answer 1

Step-by-step explanation:

length= x+9 and breadth=x, 2(x+9+x)=110m,4x+18=110m,4x=92m,x=23m,x+9=32m

Answer 2

Given :

• The length of a rectangular hall is 9 metres more than its breadth
• Perimeter of the hall = 110 m

To find :

• Length of the hall
• Breadth of the hall

Knowledge Required :-

→ Formula of perimeter of rectangle :-

• Perimeter = 2(l + b)

where,

• l = length of the rectangle
• b = breadth of the rectangle

Solution :

Here, we are given that length of the rectangular hall is 9 m more than its breadth. So, firstly we will assume any variable as the breadth of the rectangular hall and for length we will add 9 m in the variable.

Let,

• Breadth of the rectangular hall = x m
• Length of the rectangular hall = x + 9 m

Substituting the values in the formula of perimeter of rectangle,

⠀⠀⠀⇒ 110 = 2(x + 9 + x)

⠀⠀⠀⇒ 110/2 = x + 9 + x

⠀⠀⠀⇒ 55 = 2x + 9

⠀⠀⠀⇒ 55 - 9 = 2x

⠀⠀⠀⇒ 46 = 2x

⠀⠀⠀⇒ 46/2 = x

⠀⠀⠀⇒ 23 = x

The value of x = 23

Substitute the value of x in the breadth and length of the rectangular hall.

→ Length = x + 9 = 23 + 9 = 32 m

→ Breadth = x = 23 m

━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀Verification :-

Perimeter = 110

Substitute the value of length and breadth in the formula of periemter of rectangle to verify their values.

⠀⠀⠀⇒ 2(32 + 23)

⠀⠀⠀⇒ 2(55)

⠀⠀⠀⇒ 110

Perimeter = 110

Hence, verified.