Question

The perimeter of rectangular field is 28 cm and its area is 48 cm^2. Find its length and
breadth​

Answer 1

Answer:

The Length and Breadth of the rectangle is 8 cm and 6 cm respectively.

Step-by-step explanation:

Perimeter = 28 cm

Area = 48 cm²

Consider the LENGTH of rectangle as x and BREADTH as y.

According to the Question,

$\rightarrow$ x × y = 48 ----- (Equation 1)

$\rightarrow$ 2(x + y) = 28

$\rightarrow$ x + y = 14 ------ (Equation 2)

$\rightarrow$ x = 14 - y

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★ Substitute the value of x in equation 1 :

$\rightarrow$ (14 – y) × y = 48

$\rightarrow$ 14y – y² = 48

$\rightarrow$ –y² + 14y – 48 = 0

$\rightarrow$ y² – 14y + 48 = 0

$\rightarrow$ y² – 8y – 6y + 48 = 0

$\rightarrow$ y(y – 8) – 6(y – 8) = 0

$\rightarrow$ (y – 6)(y – 8)

$\rightarrow$ y = 6 or y = 8

Length of the rectangle = 8 cm

____________________

★ Substitute value of y in equation 2 :

$\rightarrow$ x + 8 = 14

$\rightarrow$ x = 14 – 8

$\rightarrow$ x = 6

Breadth of the rectangle = 6 cm

Therefore, the Length and Breadth of the rectangle is 8 cm and 6 cm respectively.

Answer 2

Answer :

• Length = 6 or 8.
• Breadth = 6 or 8.

Step by step explanation :

Given that :

• Perimeter of Rectangular field is 28cm.
• Area of Rectangular field is 48cm².

To Find :

• Length and breadth the rectangular field.

Formulas Used :

• Perimeter (Rectangle) = 2(length+ breadth)
• Area (Rectangle) = length × breadth

Finding length and breadth :

Perimeter (Rectangle) :

• 2 (l+b)

• 28 = 2(l+b)
• 14 = l+b
• l = 14-b [Let it be eq. 1]

Area (Rectangle) :

• length × breadth

• 48 = (14-b) × breadth
• 48= 14b-b²
• 48-14b+b²
• b²-14b+48=0
• b²-8b-6b+48=0
• b(b-8)-6(b-8)=0
• (b-6)(b-8)
• b= 6 or b=8

.°. b = 6 or 8.

Length :

• 14- 8 or 14-6
• 6 or 8.

.°. l = 6 or 8.

Method Used :

• First we apply perimeter of Rectangle formula (i.e. 2 (l+b)) and hence, from here we will convert whole Equation in terms of length or breadth. Now ,we will apply area of Rectangle formula (i.e. l × b) and here we will substitute value which we find from above .