Question

${\fcolorbox{blue}{black}{\pink{\:\:\:\:\:\:\:\:\ Question\:\:\:\:\:\:\:\:\:\:\:\:}}}$

If length is 3 times of its breadth of rectangle perimeter is 200 cm Find its length and breadth?


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Answer 1

◈ Given ◈

If length is 3 times of its breadth of rectangle perimeter is 200 cm

◈ To find ◈

• Length & breadth of rectangle

◈ Solution ◈

It is given that if length is 3 times of its breadth of rectangle.

So let breadth be x and length be 3x

$\\\bullet\:\sf Perimter\: of \: rectangle = 200 cm$

$\quad\quad{\underline{\mathfrak{\red{\qquad{As\:we\:that\qquad}}}}}$

$\: \: \: {\blue{\boxed{\bf{\blue{Perimeter\:of\:rectangle=2(l + b)}}}}}$

Where,

• l = length
• b = breadth

$\\\qquad{\underline{\mathfrak{\red{\qquad{According\:to\:question\qquad}}}}}$

$\implies\sf Perimter\:of\:rectangle = 200cm$

$\implies\sf 2(l + b) = 200$

$\implies\sf 3x + x = \cancel\dfrac{200}{2}$

$\implies\sf 4x = 100$

$\implies\sf x = \cancel\dfrac{100}{4}$

$\implies\sf x = 25$

$\therefore{\underline{\boxed{\bf{Breadth\:of\:rectangle\: = x = 25cm}}}}$

$\therefore{\underline{\boxed{\bf{Length\:of\:rectangle\: = 3x = 75cm}}}}$

$\:$____________________________________________

Answer 2

Answer:

Given :-

• The length is 3 times of its breadth of a rectangle and the perimeter is 200 cm.

To Find :-

• What is the length and breadth of a rectangle.

Formula Used :-

${\red{\boxed{\small{\bold{Perimeter\: of\: Rectangle =\: 2(Length + Breadth)}}}}}$

Solution :-

Let, the breadth of a rectangle be x cm

And, the length of a rectangle will be 3x cm

Given :

• Length = 3x cm
• Breadth = x cm

According to the question by using the formula we get,

⇒ $\sf 2(3x + x) =\: 200$

⇒ $\sf 6x + 2x =\: 200$

⇒ $\sf 8x =\: 200$

⇒ $\sf x =\: \dfrac{\cancel{200}}{\cancel{8}}$

➠ $\sf\bold{\purple{x =\: 25\: cm}}$

Hence, the required length and breadth are,

✧ Breadth = x = 25 cm

✧ Length = 3x = 3 × 25 = 75 cm

$\therefore$ The length and breadth of a rectangle is 75 cm and 25 cm respectively.

VERIFICATION :-

↦ $\sf 2(3x + x) =\: 200$

↦ $\sf 6x + 2x =\: 200$

By putting x = 25 we get,

↦ $\sf 6(25) + 2(25) =\: 200$

↦ $\sf 150 + 50 =\: 200$

↦ $\sf\bold{200 =\: 200}$

➦ LHS = RHS

Hence, Verified ✔