Question

The length and the breath of a rectrangle are in the ratio 3:2.if the area of the rectrangle is 216 sq m,then find the length and breadth of the rectrangle and also find the perimeter.

Answer 1

Answer:

length is 18m

breadth is 12 m

perimeter is 60m

Step-by-step explanation:

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Answer 2

Answer :-

• Length of the rectangle = 18 m.
• Breadth of the rectangle = 12 m.

• Perimeter of the rectangle = 60 m.

To find :-

• The length and breadth of the rectangle.

• The perimeter of the rectangle.

Solution :-

• It is given that the length and breadth of a rectangle are in the ratio 3 : 2 and the area of the rectangle is 216 m².

Let :-

• The length and breadth of the rectangle be 3x and 2x respectively, as they are in the ratio 3 : 2.

Now, we know that :-

$\underline{ \boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth}}$

Here,

• Length = 3x.
• Breadth = 2x.
• Area = 216 m².

Substituting the given values in this formula,

$\implies \rm3x \times 2x = 216$

$\rm\implies {6x}^{2} = 216$

$\rm \implies {x}^{2} = \dfrac{216}{6}$

$\rm\implies {x}^{2} = 36$

$\rm \implies x = \sqrt{36}$

$\implies \overline{ \boxed{ \rm x = 6 \: m}}$

Hence :-

$\bf Length = 3x = 3 \times 6 = 18 \: m.$

$\bf Breadth = 2x = 2 \times 6 = 12 \: m.$

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• Now, let's find the perimeter of the rectangle!

We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Length = 18 m.
• Breadth = 12 m.

Therefore,

$\hookrightarrow \tt Perimeter = 2 \: (18 + 12)$

$\hookrightarrow\tt Perimeter = 2 \: (30)$

$\tt\hookrightarrow Perimeter = 2 \times 30$

$\hookrightarrow \overline{ \boxed{ \tt Perimeter = 60 \: m}}$

Hence :-

• The perimeter of the rectangle is 60 m.

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