The perimeter of a rectangle is 22 cm and area is 30 sq. cm. What is the difference of length and breadth?
Answers
Area = L x b
30 = L x b
b = 30 / L
perimeter = 2(L + b)
22= 2(L + b)
by putting the value of b
22 = 2( L + 30/ L)
11L = L ^ 2 +30
L^2 -11L +30 = 0
L^2 - 5L - 6L + 30 = 0
L (L -5) - 6 (L -5)=0
(L-5)(L-6)
L = 5,6
by putting the value of L
b= 30/ 6 = 5cm
The difference between
L-b =6-5 =1
Answer:
The difference of length and breadth is 1 cm
Step-by-step explanation:
The perimeter of a rectangle is 22 cm
The area of a rectangle is 30 cm²
The perimeter of a rectangle = 2 (l + b)
22 = 2 (l + b)
⇒ 2l + 2b = 22
Divide by 2
⇒ l + b = 11
⇒ l = (11 - b)
Area = l × b
l × b = 30
Substitute the value of l
⇒ l = (11 - b)
⇒ (11 - b) b = 30
⇒ - b² + 11b = 30
⇒ - b² + 11b - 30 = 0
⇒ - 1 (- b² + 11b - 30) = 0
⇒ b² - 11b + 30 = 0
⇒ b² - 5b - 6b + 30 = 0
⇒ b (b - 5) - 6 (b + 5) = 0
⇒ (b - 5) (b - 6)
∴Breadth = 5 cm
Length = 6 cm
The difference of length and breadth :
⇒ Length = 6 cm
⇒ Breadth = 5 cm
⇒ 6 - 5 = 1
Therefore ,
The difference of length and breadth is 1 cm