Question

A rectangle and a square have the same perimeter 100 cm. Find the side of the square. If the rectangle has a breadth 2 cm less than that of the square. Find the breadth, length and area of the rectangle.​

Answer 1

❥Answer :-

Perimeter of square and rectangle is 100cm .

❥To find the side of square

100cm = 4×side

side = 100/4 = 25

side = 25cm

❥Breadth of rectangle = 2cm less then side of square

Breadth = 25 - 2

Breadth = 23cm

❥Length of rectangle

2( l + b) = 100

2( l + 23) = 100

l + 23 = 100/2

l + 23 = 50

l = 50 - 23

l = 27

❥To find area of rectangle

length × breadth

27 × 23

621 cm²

length of rectangle = 27cm

area of rectangle = 621cm²

Answer 2

⠀Given Question -

A rectangle and a square have the same perimeter 100 cm. Find the side of the square. If the rectangle has a breadth 2 cm less than that of the square. Find the breadth, length and area of the rectangle.

Stated -

• Rectangle and square have same perimeter 100cm
• Breadth of rectangle is 2cm less than square

To Attain -

• Side of Square
• Breadth of Rectangle
• Length of Rectangle
• Area of Rectangle

Formulae to be used -

• Area of rectangle = lb sq.units
• Perimeter of rectangle = 2(l + b)

Where -

• L stands for length
• B stands for breadth

Diagram -

For square, having side of 25cm.

$\begin{gathered}\begin{gathered}\begin{gathered} \: \: \: \sf{25cm \: \: }\boxed{\begin{array}{cc}\\\\\\ \sf\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\:\:\:\:\:}\\ \end{array}} \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 25cm}\end{gathered}\end{gathered}\end{gathered}$

For rectangle, having length - 27cm and breadth - 23cm

$\begin{gathered}\begin{gathered}\begin{gathered} \: \: \: \sf{23cm \: \: }\boxed{\begin{array}{cc}\\\\\\ \sf\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\:\:\:\:\:}\\ \end{array}} \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 27cm}\end{gathered}\end{gathered}\end{gathered}$

Explanation -

⠀— In the question, It is concluded that both rectangle and square are sharing same perimeter as 100cm. 2nd statement says that if both are sharing same perimeter then what should be the side of square. Simply, breadth of rectangle is 2cm less than side of square. So, what should be the breadth, length and area of the rectangle. Let's find it by appropriate method.

Solution -

⠀It is given that; the perimeter of square is 100cm so, we need to find its side first.

$:\implies\sf Side \: of \: square = {\dfrac{Perimeter}{4}}$

$:\implies\sf \: Side = {\dfrac{100}{4}}$

$:\implies\sf{Side\:=\: 25cm}$

Hence, Required side of Square is 25cm.

Now, -

⠀If breadth is 2cm less than side of square than..

$:\implies\sf{Breadth = 25 - 2}$

$:\implies\sf{Breadth = 23cm}$

⠀— Required breadth is 23cm.

Now, -

⠀After that; As given in the given, perimeter of rectangle is too 100cm but we don't know the actual length. It is still unknown . So before, let's find the length.

$:\implies\sf{Perimeter\; of\;rectangle = 100}$

$:\implies\sf{ 2 \times (length + breadth) = 100}$

$:\implies\sf{length\;+\;breadth = \dfrac{100}{2}}$

$:\implies\sf{length\;+\;breadth = 50}$

But, Breadth is 23cm.

$:\implies\sf{Length = 50 - 23 }$

$:\implies\sf{Length = 27cm}$

Since, -

⠀We got our required length & breadth according to the question, but now we have to find the area of rectangle by using its formula.

$:\implies\sf{Area_{\;(rectangle)} = lb \: sq.units }$

$:\implies\sf{Area\; = 27cm \times 23cm }$

$:\implies\sf{Area\; = 621\;sq.cm }$

⠀

Final Answer -

⠀⠀$\twoheadrightarrow$ Hence, Side of the square is 25cm. Length & breadth of the rectangle is 27cm & 23cm. Area of the given rectangle 621cm².

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