Question

The length of a marriage hall is 4 times its breadth. If
the perimeter of the hall is 240m, find the length and the
breadth of the marriage hall.

Answer 1

Hey friend,

Here is the solution :-

$let \: the \: breadth \: of \: the \: room = \: x \\ then \: length \: is \: 4 \times x = 4x \\ \\ perimeter \: is \: given \: as \: 240 \: m \\ \\ perimeter \: of \: a \: rectangle = 2(l + b) \\ \\ 240 = 2(4x + x) \\ \\ 240 = 2(5x) \\ \\ 240 = 10x \\ \\ \frac{240}{10} = x \\ \\ x = 24 \: m \: (breadth) \\ 4x = 4 \times 24 = 96 \: m \: (length)$

$so \: the \: length \: of \: the \: \\ marriage \: hall \: is \: 96 \: m \\ and \: the \: breadth \: is \: 24 \: m$

I hope this will help you....

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\purple{Answer:}}}}}}$

$\bf{\underline{\sf{\blue{Given:}}}}$

• The length of a marriage hall is 4 times its breadth.
• The perimeter of the hall is 240m

$\bf{\underline{\sf{\blue{To\:find:}}}}$

• Length of the marriage hall
• Breadth of the marriage hall

$\bf{\underline{\sf{\blue{Solution:}}}}$

Let's assume the marriage hall to be rectangular shaped.

Let the breadth of the marriage hall be x m

$\bf{\underline{\sf{\pink{As\:per\:first\:condition\::}}}}$

• The length of a marriage hall is 4 times its breadth

Length = 4x m

We know that perimeter of a rectangle is calculated using the formula,

$\bf{\large{\underline{\boxed{\sf{\green{Perimeter\:of\:a\:rectangle \:=\:2\:(\:l\:+\:b\:}}}}}}$

Perimeter = 240m

Plug in the values in the formula,

=>$\sf {240 = 2 ( l + b) }$

=> $\sf{240 = 2 ( 4x + x)}$

=> $\sf{240 = 2 (4x) + 2 (x) }$

=> $\sf{240 = 8x + 2x }$

=> $\sf{240 = 10x }$

=> $\sf\frac{240}{10}$ = x

=> 24 = x

•°• Putting the value of x in the value of length,

Length = 4x = 4 × 24 = 96 m

Breadth = x = 24 m

$\bf{\huge{\underline{\boxed{\sf{\orange{Verification:}}}}}}$

Length = 96 m

Breadth = 24 m

Perimeter = 240 m

Plug in the values in the formula for perimeter of the rectangle.

=>$\sf { 240 = 2 ( l + b)}$

=> $\sf{240 = 2 ( 96 + 24) }$

=> $\sf{240 = 2 (120) }$

=> $\sf{240 = 240 }$

LHS = RHS.

Hence verified.