Question

(1) The perimeter of a rectangle is 200 cm. Its length is three times its breadth. Find it
length and breadth.​

Answer 1

❍ Let the Breadth of the rectangle be x than, Length of the rectangle is 3x respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀

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$\star\;\boxed{\sf{\pink{Perimeter_{\:(rectangle)} = 2(l + b)}}}$

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• Here, l is length of the rectangle and b is the Breadth of the rectangle.
• Given perimeter of the rectangle is 200 cm.

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Therefore,

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$:\implies\sf Perimeter = 2(Length + Breadth) \\\\\\:\implies\sf 200 = 2(3x + x) \\\\\\:\implies\sf 200 = 6x + 2x\\\\\\:\implies\sf 200 = 8x\\\\\\:\implies\sf x = \cancel\dfrac{200}{8}\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 25}}}}}\;\bigstar$

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Hence,

• Length of the rectangle, 3x = 3(25) = 75 cm.

• Breadth of the rectangle, x = 25 cm.

$\therefore{\underline{\sf{Hence, \; length \; and \; Breadth\; of \; rectangle\; are\; \bf{ 75cm\;\&\;25cm}.}}}$

Answer 2

Answer:

• Length = 75cm.
• Breadth = 25cm.

Given:

• The perimeter of a rectangle is 200 cm.
• Its length is three times its breadth.

To find:

• Find it's length and breadth.

Solution:

Given that,

Its length is three times its breadth.

Let us assume length as l

And, Let us assume breadth as b

So,

It can be written as l = 3b

We know that,

Perimeter of a rectangle = 2(l + b)

Now,

l × b = 200

• Given, Perimeter = 200.

We know that, l = 3b..

By replacing 3b in place of l, We get :

➨ 2(3b + b) = 200

➨ 6b + 2b = 200

➨ 8b = 200

➨ b = $\bf \dfrac{200}{8}$

➨ b = 25cm.

Hence,

Breadth = 25cm.

Length = 3b = 3 × 25 = 75cm.

Verification:

2(3b + b) = 200

➨ 2(3(25) + 25) = 200

➨ 2( 75 + 25 ) = 200

➨ 2( 100 ) = 200

➨ 200 = 200

LHS = RHS

Hence , Verified.