Question

the perimeter of a rectangle is equal to the perimeter of a square. Twice the length of the rectangle is equal to 3 times, it's breadth. If one side of the square measures 100 cm. find the length and the breadth of the rectangle​

Answer 1

Let:

• Lenght of rectangle be = l
• Breadth of rectangle be= b

Given:

• Twice the length of the rectangle is equal to 3 times, it's breadth

Thus,

$\bold{\boxed{\purple{2l= 3b----i}}}$

━━━━━━━━━━━━━━━━

Also given:

• Perimeter of Rectangle = Perimeter of Square
• Side of square = 100cm

Thus,

4 × side of square = 2×( length + breadth)

⟹ 4 × 100cm = 2× ( l + b)

⟹ 400cm = 2l + 2b

⟹( 3b) +2 b =400 cm [from i we know 2l=3b]

⟹5b= 400cm

$\red{\bold{\boxed{\large{\implies b = breadth= 80cm}}}}$

━━━━━━━━━━━━━━━━

Now by substituting b= 80 in the equation i,

2l=3b

⟹2l= 3× 80cm

⟹ 2l= 240cm

$\red{\bold{\boxed{\large{\implies l = length= 120 cm}}}}$

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

The perimeter of a rectangle is equal to the perimeter of a square. Twice the length of the rectangle is equal to 3 times, it's breadth. If one side of the square measures 100 cm. find the length and the breadth of the rectangle

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• The perimeter of a rectangle is equal to the perimeter of a square.
• Twice the length of the rectangle is equal to 3 times, it's breadth.
• One side of the square measures 100 cm.

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• The length and the breadth of the rectangle.

${\bigstar}\large{\boxed{\sf{\pink{Answer}}}}$

Length = 120 cm

Breadth = 80 cm

${\bigstar}\large{\boxed{\sf{\pink{We \: also \: write \: that}}}}$

$\implies$ Length as L

$\implies$ Breadth as B

$\implies$ Perimeter as P

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

$\large\purple{\texttt{We know that we have to find L nd B}}$

$\large\blue{\texttt{Given that Twice the L = Trice the B}}$

$\large\purple{\texttt{We also know that,}}$

$\large{\boxed{\sf{\: \: Perimeter \: of \: square}}}$

$\large{\boxed{\boxed{\sf{4 × sides}}}}$

$\large{\boxed{\sf{\: \: Perimeter \: of \: rectangle}}}$

$\large{\boxed{\boxed{\sf{2[l+b]}}}}$

$\large\blue{\texttt{Given that P of square = P of rectangle}}$

$\large\purple{\texttt{Now we have to follow the steps →}}$

$\mapsto$ 4 × sides = 2 (l+b)

$\mapsto$ 4 × 100 = 2 (l+b)

$\mapsto$ 400 = 2l + 2b

$\mapsto$ 3b + 2b = 400

$\mapsto$ 5b = 400

$\mapsto$ b = 400/5

$\mapsto$ b = 80 cm

Hence, breadth = 80 cm.

$\huge{\boxed{\sf{Breadth \: = \: 80 \: cm}}}$

$\large\purple{\texttt{Now we have to follow the steps →}}$

$\mapsto$ 2l = 3b

$\mapsto$ 2l = 3 × 80

$\mapsto$ 2l = 240

$\mapsto$ l = 240/2

$\mapsto$ l = 120 cm

Hence, length = 120 cm.

$\huge{\boxed{\sf{Length \: = \: 120 \: cm}}}$

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@Itzbeautyqueen23

Hope it's helpful !

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