In a rectangular field, the sum of the length and the breadth is 9 cm, and the area is 18 cm2. If the length is 'a' and breadth is 'b', then find the value of (a2 − ab + b2).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 27.
The length and breadth of the rectangular field are a and b, respectively.
So, a + b = 9 .....(1)
The area of a rectangle = Length × Breadth = ab = 18 .....(2)
From equation (1),
⇒ (a + b)2 = 92
⇒ a2 + 2ab + b2 = 81
⇒ a2 + 2(18) + b2 = 81
⇒ a2 + b2 = 81 - 36 = 45 .....(3)
Now, (a2 - ab + b2) = 45 - 18 = 27