Question

4. The perimeter and area of a rectangle are
22 cm and 30 cm² respectively. Find the
length and breadth of the rectangle.​

Answer 1

Answer:

Length= 6cm

Breadth= 5cm

Step-by-step explanation:

2(l+b) = 22 lb = 30

l+b=11 lb=30

l^2 + b^2 + 2lb = 121

l^2 + b^2 + 60 = 121

l^2 + b^2 = 121-60

l^2 + b^2 - 60 = 121-60-60 = 1

l-b = 1

As l+b = 11 & l-b=1

So, l = 6 & b = 5

Answer 2

Answer:

Length of the rectangle is 6 cm and the breadth of the rectangle is 5 cm.

Step-by-step explanation:

Given :-

• The perimeter of the rectangle is 22 cm.
• The area of the rectangle is 30 cm².

To find :-

• Length and breadth of the rectangle.

Solution :-

Formula used :

★ Perimeter of the rectangle = 2(l+b)

★ Area of the rectangle = l × b

Consider,

• Length = x cm
• Breadth = y cm

According to the 1st condition,

2 ( l + b) = 22

→ 2(x+y) = 22

→ x+y = 11

→ x = 11-y.................(i)

According to the 2nd condition,

xy = 30

→ (11-y)y = 30 [ Put x = 11-y from eq (I)]

→ 11y - y² = 30

→ -y²+11y - 30 = 0

→ y² -11y + 30 = 0

→ y² -(6+5)y+30=0

→ y²-6y-5y+30=0

→ y (y-6) - 5(y-6) = 0

→ (y-6) (y-5) = 0

Either,

y - 6 = 0

→ y = 6

Or,

y-5 = 0

→ y = 5

★ Breadth of the rectangle is 5 cm.

Now put y = 5 in eq(I) for getting the value of x.

x = 11-y

→ x = 11-5

→ x = 6

★ Length of the rectangle is 6 cm.