Question

|(a) The length of a rectangle is three times the breadth and its area is 300 cm2. Find the
length and breadth of the rectangle.
​

Answer 1

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Question :-

The Length of a rectangle is three times the breadth of the rectangle . If the area of the rectangle is 300 cm² . Find the length and breadth of the rectangle .

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Answer :-

Given :-

Length of the rectangle is three times the breadth .

Area of the rectangle = 300 cm²

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Required to find :-

• Length of the rectangle ?
• Breadth of the rectangle ?

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Formula used :-

$\large{\underline{\boxed{\mathrm{Area \; of \; the \; rectangle \; = length \times breadth }}}}{\bigstar}$

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Solution :-

Given that ;

Length of the rectangle is three times the breadth .

So,

Let, the breadth be " x " cm .

Length is thrice the breadth .

Hence, let the length be " 3x " cm .

So, here we have to use an formula .

The formula is ,

$\large{\orange{\underline{\boxed{\mathrm{Area \; of \; the \; rectangle \; = length \times breadth }}}}}{\bigstar}$

So,

According to problem :-

Length x. breadth = Area of the rectangle

$\tt{3x \;cm \times x \; cm = 300 \; {cm}^{2}}$

$\tt{3{x}^{2}\; {cm}^{2} = 300 {cm}^{2}}$

Now transpose 3 to the right side

$\longrightarrow{\tt{ {x}^{2} \; {cm}^{2} = \dfrac{300 \; {cm}^{2}}{3}}}$

$\longrightarrow{\tt{ {x}^{2} \; {cm}^{2} = 100 {cm}^{2 }}}$

Here cm² will get cancelled on both sides .

So,

$\longrightarrow{\tt{ {x}^{2} = 100 }}$

Transpose the power 2 to the right side hence we get square root .

$\longrightarrow{\tt{ x = \sqrt{100}}}$

As we know that

$\underline{\boxed{\mathrm{ {10}^{2} = 100}}}$

So,

$\longrightarrow{\red{\underline{\underline{\tt{ x = 10 \; cm}}}}}$

Now substitute this value of X in assumed values of length and breadth in order to find the actual measurements of Length and breadth .

Therefore,

$\underline{\boxed{\green{\tt{ Length \; = \; 3x \; = 3(10) = 30\;cm}}}}$

$\underline{\boxed{\green{\tt{ Breadth \;= \; x = 10 \;cm}}}}$

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➦ Please refer to the attachment given .

➦ In the attachment the white coloured figure is the rectangle with the dimensions of 3x cm & x cm .

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Answer 2

Given :

• Area of Rectangle = 300 cm²
• Length is 3 times the breadth

To Find :

• Length and breadth of rectangle

Solution :

Let length of rectangle be x m and breadth be y m.

So, breadth will be 3x m

• Length (y) = 3x
• Breadth = x

$\underbrace{\sf{Area \: of \: Rectangle}}$

$\implies \sf{Area \: = \: length \: \times \: breadth} \\ \\ \implies \sf{Area \: = \: 3x \: \times \: x} \\ \\ \implies \sf{Area \: = \: 3x^2} \\ \\ \implies \sf{3x^2 \: = \: 300} \\ \\ \implies \sf{x^2 \: = \: \dfrac{300}{3}} \\ \\ \implies \sf{x^2 \: = \: 100} \\ \\ \implies \sf{x \: = \: \sqrt{100}} \\ \\ \implies \sf{x \: = \: \pm \: 10}$

As we know that side can't be negative so we will took positive value only. So, breadth of rectangle is 10 cm

Now,

$\implies \sf{y \: = \: 3x} \\ \\ \implies \sf{y \: = \: 3 \: \times \: 10} \\ \\ \implies \sf{y \: = \: 30}$

Length of rectangle is 30 cm

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