Question

The breadth of a rectangle is 1/3 rd of its length. If the perimeter of rectangle is 64cm . find the area of rectangle.​

Answer 1

Given that,The breadth of a rectangle is 1/3 rd of its length

and the perimeter of of the rectangle is 64cm.

☯️To Find: The area of rectangle.

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$\sf { \underline{★According \: to \: the \: question : }}$

➺The breadth of the rectangle is 1/3 of its length

so,the length is three times it's breadth.!

now,let the breadth be x and the length be 3x

and as known the perimeter is 64

$\sf\blue{now\: let's\: find\: the\: values:}$

$\sf \: : ⟹ \: perimeter \: of \: a \: rectangle = 2(l + b) \\ \\ \sf \: : ⟹64 = 2(3x + x) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: : ⟹64 = 6x + 2x\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: : ⟹64 = 8x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: : ⟹x = \cancel \frac{64}{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: : ⟹x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so now,

breath = 8cm (x)

length = 24cm(3x)

$\blue {\underline{ \purple{ \boxed{ \mathfrak{ \therefore{length = 24cm \: and \: breadth = 8cm}}}}}}$

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$\sf {\red{ \underbrace{area \: of \: a \: rectangle \: = \: lenght \times breadth}}}$

$\sf \: : ⟹area = 24 \times 8cm \\ \\ \sf \: : ⟹area = 192cm\: \: \: \: \:$

$\blue {\underline{ \purple{ \boxed{ \mathfrak{ \therefore \: area \: of \: the \: rectangle= 192 {cm}^{2} }}}}}$

hope this helps.!!

Answer 2

Answer :

The area of rectangle is 192cm².

Step-by-step explanation :-

To Find,

• Area of rectangle

Solution,

Given that,

• Breadth of rectangle = $\sf{\dfrac{1}{3} \times x}$ of it's length
• Perimeter of rectangle = 64cm

Let us assume the length as x and the breadth as $\sf{\dfrac{1}{3} \times x}$

As we know that,

$\dag \: \boxed{ \red{ \sf{Perimeter \: of \: rectangle = 2(l + b)}}}$

Where,

• l = Length
• b = Breadth

Therefore,

$\sf{ \mapsto \: 2(l + b) = 64} \\ \\ \\ \sf{ \mapsto \: 2 \: \bigg( \: x + \dfrac{x}{3} \bigg) = 64} \\ \\ \\ \sf{ \mapsto \: \bigg( \: \dfrac{x + 3x}{3} \bigg) = \dfrac{64}{2}} \\ \\ \\ \sf{ \mapsto \: \dfrac{4x}{3} = \cancel{\dfrac{64}{2}}} \\ \\ \\ \sf{x = \dfrac{32 \times 3}{4}} \\ \\ \\ \sf{ \mapsto \: x = \dfrac{ \cancel{32} \times 3}{ \cancel{4}}} \\ \\ \\ \sf{ \mapsto \: x = 8 \times 3} \\ \\ \\ \bf{ \mapsto \: x = 24}$

The value of x is 24.

Now, the length and breadth is,

We assumed length as x, So, length is,

$\sf{ \mapsto \: x = 24} \\ \\ \sf{ \mapsto \: length = 24 \times 1} \\ \\ \bf{ \mapsto \: length = 24}$

The length of Rectangle is 24cm.

Now, breadth is,

We assumed breadth as $\sf{\dfrac{1}{3} \times x}$

Therefore,

$\sf{\mapsto \: \dfrac{1}{3} \times x} \\ \\ \sf{\mapsto \: \dfrac{1}{3} \times 24} \\ \\ \sf{\mapsto \: \dfrac{1}{ \cancel{3}} \times \cancel{24}} \\ \\ \sf{\mapsto \: 8} \: \: \: \: \: \: \: \: \: \:$

The breadth of Rectangle is 8cm.

ACCORDING THE QUESTION,

Area of rectangle is, as we know that,

$\dag \: \boxed{ \red{ \sf{Area \: of \: rectangle = (l \times b)}}}$

Therefore,

$\sf{ \mapsto \: l \times b} \\ \\ \\ \sf{ \mapsto \: 24 \times 8} \\ \\ \\ \frak{ \pink{\mapsto \: 192{cm}^{2}}} \: \: \: \: \bigstar$

Hence, area of rectangle is 192cm².