Question

length and breadth of rectangular room is in the ratio of 7:4 if the perimeter of the room is 132 cm . Find the length and breadth of room ​

Answer 1

Answer:

let length-7x

breadth-4x

perimeter of rect=2(l+b)

2×11x=132

x=132/22

x=6

Step-by-step explanation:

length=7×6=42

breadth=4×6=24

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Answer 2

Given : Length and breadth of rectangular room is in the ratio 7 : 4 and perimeter of the room is 132cm.

To Find : Length and breadth of the room.

⠀⠀⠀⠀⠀⠀⠀⠀ _______________

Let the length and breadth of the rectangle be 7x and 4x respectively.

$\:$

As we know that :

$\: \:$

$\underline{\boxed{\sf\purple{\bigstar \: perimeter \: of \: a \: rectangle \: = 2(l + b)}}}$

$\: \:$

Where

$\: \:$

• l denotes length of the rectangle.
• b denotes breadth of the rectangle.

$\: \:$

Put the values in the formula and solve -

$\: \:$

$\sf:\implies \: Perimeter_{(rectangle)} = 2(l + b) \\ \\ \\ \sf:\implies \: 132 = 2(7x + 4x) \\ \\ \\ \sf:\implies \: \frac{132}{2} = 11x \\ \\ \\ \sf:\implies \: 11x = 66 \\ \\ \\ \sf:\implies \: x = \cancel\frac{66}{11} \\ \\ \\ \sf:\implies \: x = \underline{\boxed{\sf\purple{6}}}\bigstar$

$\: \: \: \:$

Put the value of x in the ratio

$\: \:$

• Length of the rectangle = 7x = 7(6) = 42cm
• Breadth of the rectangle = 4x = 4(6) = 24cm

$\: \: \\ \\ \: \:$

$\sf\therefore{\underline{Hence, \: the \: length \:and\: breadth \: of \: the \: rectangle \: are \: \bold{42cm} \: and \: \bold{24cm}respectively}}$