Question

The area of rectangle is 21 cm^2 and its perimeter is 20cm.the length and breadth of the rectangle are to be found

Answer 1

Given :

• Area = 21 cm²
• Perimeter = 20cm

To Find :

• Length & Breadth of the Rectangle

Answer

2(l + b) = 20

l + b = 20/2

l + b = 10

Thus,

Length = 7cm

Breadth = 3cm

Formula Used

Perimeter of Rectangle = 2(l+b)

Area of Rectangle = l × b

Here,

l = Length

b = Breadth

We get the first equation as l + b = 20

l + b = 10

Square on both the sides

$\bf l^{2} + b^{2} + 2lb = 100$

We will get answer as zero

$\bf l^{2}+ b^{2} + 2(21) = 100$

$\bf l^{2} + b^{2} = 58$

We also know

$\bf a^{2} + b^{2} = (a - b)^{2} + 2ab$

Putting it

And subtracting 2lb from both the sides

(l - b)² + 2lv - 2lb = 58 -2lb

(L - b)² = 58 - 42

L - b = √16

L - b = 4..(ii)

Putting the equation

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀l + b = 10

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀l - b = 4

⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ——————

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀2 l = 14

Thus,

L = 7

B = 3

Additional Information

Area of rectangle = length × breadth

Area of square = (side)²

Area of rhombus = ½ × base × height

Area of trapezium = ½ × sum parallel sides × height

Area of Parallelogram = base × height

Answer 2

Given :

• The area of rectangle is 21 cm² .
• Its perimeter is 20 cm.

To find :

• Length and breadth of the rectangle.

Solution :

Consider ,

• Length of rectangle = x cm
• Breadth of rectangle = y cm

Formula Used :-

★ ${\boxed{\sf{Area\:of\: rectangle=length\times\: breadth}}}$

★ ${\boxed{\sf{Perimeter\:of\: rectangle=2(length+breadth)}}}$

According to the 1st condition :-

• Area of the rectangle is 21 cm.

$\to\sf{xy=21..............(i)}$

According to the 2nd condition :-

• Perimeter of rectangle is 20 cm.

$\to\sf{2(x+y)=20}$

$\to\sf{x+y=10}$

$\to\sf{x=10-y.................(ii)}$

Now take eq(i) and put x=10-y from eq(ii) .

$\sf{xy=21}$

$\to\sf{(10-y)y=21}$

$\to\sf{10y-y^2=21}$

$\to\sf{-y^2+10y-21=0}$

$\to\sf{y^2-10y+21=0}$

$\to\sf{y^2-(7+3)y+21=0}$

$\to\sf{y^2-7y-3y+21=0}$

$\to\sf{y(y-7)-3(y-7)=0}$

$\to\sf{(y-7)(y-3)=0}$

Either,

y - 7 = 0

→ y = 7

Or,

y - 3 = 0

→ y = 3

Now put y = 3 in eq (ii).

x = 10-y

→ x = 10-3

→ x = 7

Therefore ,

• Length = 7 cm
• Breadth = 3 cm.