Question

the perimeter of a rectangle is 42cm and its area is 20sq.cm. a)find the sum of the length and breadth?
b)find the length? and breadth? ​

Answer 1

Answer:

Step-by-step explanation:

(a) Perimeter=42 cm

Perimeter = 2(l+b)

42/2 cm = l+b

21 cm = length +breadth

Answer 2

Answer :-

• l = 20cm , b = 1cm
• l + b = 21cm

Given :-

• The perimeter of a rectangle is 42cm and its area is 20cm².

To Find :-

• Sum of length and breadth
• length and breadth

Solution :-

As we know that

• Perimeter of a rectangle = 2 (l + b)
• Area of the rectangle = l × b

Where

• l = length
• b = breadth

Put those in the equation

• 2 (l + b) = 42 ...i)
• l × b = 20 ...ii)

l × b = 20

l = 20/b

Put the value of l in eq i)

Now

⇒ 2 (l + b) = 42

⇒ 2 (20/b + b) = 42

⇒ 2 (20 + b²/b) = 42

⇒ 20 + b² /b = 42/2

⇒ 20 + b²/b = 21

⇒ 20 + b² = 21b

⇒ 20 + b² - 21b = 0

⇒ b² - 21b + 20 = 0

Now split the middle term

⇒ b² - 20b - b + 20 = 0

⇒ b (b - 20) - 1 (b - 20) = 0

⇒ (b - 1) (b - 20) = 0

___________________

⇒ b - 1 = 0

⇒ b = 0 + 1

⇒ b = 1

⇒ b - 20 = 0

⇒ b = 20 + 0

⇒ b = 20

___________________

Put the value [ b = 1 ] in eq ii)

⇒ l × 1 = 20

⇒ l = 20/1

⇒ l = 20

Now

• l = 20cm
• b = 1cm

Sum of length and breadth :-

→ 20+ 1 = 21

Hence

• l = 20cm , b = 1cm
• l + b = 21cm