Question

The length of a rectangular field is 8 m and breadth is 2 m. If a square field has the same perimeter as this rectangular field,find which field has the greater area.

Answer 1

Given:

• Length of Rectangle field = 8m
• Breadth of Rectangle field = 2m
• Perimeter of square field = Perimeter of Rectangle field

Find:

• Which field has the greater area?

Solution:

we, know that

$\underline{ \boxed{ \color {purple} \rm Perimeter \: of \: Rectangle = 2(l + b)}}$

and

$\underline{ \boxed{ \color {red} \rm Perimeter \: of \: square = 4 \times (side)}}$

$\mathbb{ \color{blue}ACCORDING \: TO \: QUESTION}$

Perimeter of Square = Perimeter of Rectangle

$\rm \implies 4 \times (side) = 2(l + b)$

where,

• Length of Rectangle = 8m
• Breadth of Rectangle = 2m

So,

$\rm \implies 4 \times (side) = 2(8 + 2)$

$\rm \implies 4 \times (side) = 2(10)$

$\rm \implies 4 \times (side) = 20$

$\rm \implies side= \frac{ \cancel{20}}{ \cancel{4}} = 5m$

Hence, the side of the square will be 5m

Now,

we, know that

$\underline{ \boxed{ \color {green} \rm Area \: of \: Rectangle = l \times b}}$

where,

• Length = 8m
• Breadth = 2m

So,

$\rm \to Area \: of \: Rectangle = l \times b$

$\rm \to Area \: of \: Rectangle = 8 \times 2$

$\rm \to Area \: of \: Rectangle = 16 {m}^{2}$

Hence, The Area of Rectangle will be 16m²

Now,

we, know that

$\underline{ \boxed{ \color {orange} \rm Area \: of \: square = side\times side}}$

where,

• Side = 5m

So,

$\rm \to Area \: of \: square = side\times side$

$\rm \to Area \: of \: square = 5 \times 5$

$\rm \to Area \: of \: square =25 {m}^{2}$

Hence, the area of square will be 25m²

Now, we observed that

Area of Rectangle < Area of Square

So, the Area Square is greater than the Area of Rectangle By 9m²

Answer 2

$\huge \boxed {\fcolorbox{white}{pink}{Answer}}$

Length of rectangular field =8m

Breadth of rectangular field= 2m

ATQ ,

Perimeter of square= Perimeter of rectangle (1)

Let the side of square be x

By equation (1)

4×side = 2(l+b)

4x= 2(8+2)

4x=2(10)

x=20/4

x=5m

Therefore , side of square= 4m

Area of square= side ²

= 5²=25 m²

Where, Area of rectangle = l×b=8×2 = 16 m²

From above explanation

Area of square is greater than area of rectangle

$\huge\red {square \: has \: greater \: area}$