Question

A wire is in the shape of a square whose perimeter is 48cm.now the same wire is reshaped into a rectangle.find the length and the breadth of the rectangle if the ratio of the dimensions of a rectangle is 5:3?​

Answer 1

$\bf{\underline{\underline{Given}}}$

• Perimeter of the wire in the shape of square = 48 cm

• Ratio of the dimensions of the wire in the shape of rectangle = 5:3

$\bf{\underline{\underline{Assumption}}}$

Let the common multiple of ratio of wire in the shape of rectangle be x

Hence,

Length = 5x

Breadth = 3x

$\bf{\underline{\underline{Solution}}}$

The wire in the shape of square was reshaped into rectangle without providing any extra material.

Hence,

The Perimeter of wire in the shape of square = Perimeter of the wire in the shape of rectangle

Therefore,

${\boxed{\underline{\bf{4\times Side = 2(Length + Breadth)}}}}$

$\bf{4\times Side = 48}$

$\bf{\implies 48 = 2(5x + 3x)}$

$\bf{\implies \dfrac{48}{2} = 8x}$

$\bf{\implies 8x = 24}$

$\bf{\implies x = \dfrac{24}{8}}$

$\bf{\implies x = 3}$

Hence,

$\bf{Length = 5x = 5\times3 = 15\:cm}$

$\bf{Breadth = 3x = 3\times3 = 9\:cm}$

$\bf{\underline{Dimension\:of\:wire\:in\:the\:shape\:of\:rectangle}}$

${\underline{\boxed{\bf{Length = 15\:cm}}}}$

${\underline{\boxed{\bf{Breadth = 9\:cm}}}}$

$\bf{\underline{\underline{Additional\:Information}}}$

• $\bf{Perimeter\:of\:Square = (4\times Side)\:units}$

• $\bf{Perimeter\:of\:Rectangle = 2(Length + Breadth)\:units}$

• $\bf{Area\:of\:square = (Side)^2\:\:sq.units}$

• $\bf{Area\:Of\:rectangle = (Length\times Breadth)\:sq.units}$

Answer 2

Given :-

Perimeter of the wire in the shape of square = 48 cm

Ratio of the dimensions in the shape of rectangle= 5 : 3

To Find :-

The length of the rectangle.

The breadth of the rectangle.

Analysis :-

Consider the common ratio as a variable.

Multiply the variable to the length and breadth as per given in the ratio.

Since the perimeter of the square and rectangle are equation and the perimeter is given, you can substitute the values in it's respective formula.

Find the value of the variable accordingly and substitute it in the ratio and you'll get the dimensions easily.

Solution :-

We know that,

• l = Length
• b = Breadth
• p = Perimeter
• s = Side

Consider the common ratio as x. Then the dimensions would be 5x and 3x.

Perimeter of wire in the shape of square = Perimeter of the wire in the shape of rectangle

According to the question,

$\underline{\boxed{\sf 4 \times Side=2(Length+Breadth)}}$

Given that,

• Perimeter (p) = 48 cm

• Length (l) = 5x

• Breadth (b) = 3x

Substituting their values,

2(5x + 3x) = 48

2 × 8x = 48

8x = 48/2

8x = 24

x = 24/8

x = 3

Finding the dimensions,

Length = 5x

= 5 × 3 = 15 cm

Breadth = 3x

= 3 × 3 = 9 cm

Therefore, the length and breadth are 15 cm and 9 cm respectively.