Case Study Questions Class 7 Maths – Algebraic Expressions
CBSE Class 7 Case Study Questions Maths Algebraic Expressions. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Algebraic Expressions.
Directions (Questions 1 to 4): Examine the following case study carefully and answer the questions that follow.
Brij owns a rectangular farmland X having length 3a2 + a2b – 2ab and perimeter 6a2 + 2a2b – 2ab -4b2. Today he purchased the adjacent farmland Y and combined the two farmlands into one. The length of his farmland now increased by a2 + ab, while the breadth remained the same.
(1) Find the breadth of farmland X.
(a) 6a2 + ab -2b2
(b) ab – 2b2
(c) 12a2 -4ab
(d) -4b2
Ans: (b) Perimeter of farmland X – 6a2 + 2a2b – 2ab – 4b2.
Length of farmland X = 3a2 + a2b – 2ab.
Now, 2 (l +b) = Perimeter (for a rectangle)
b = (1/2 × Perimeter) – 1 = ½ (6a2 + 2a2b – 2ab – 4b2) – (3a2 + a2b – 2ab)
= (3a2 + a2b – ab – 2b2) – (3a2 + a2b – ab – 2b2) – (3a2 + a2b – 2ab)
= (3a2 +a2b – ab – 2b2 – 3a2 – a2b + 2ab) = ab – 2b2.
= ab – 2b2.
(2) Find the length of the combined farmland.
(a) 4a2 –ab + a2b
(b) a2 + 2ab -2b2
(c) 2a2 -3ab + a2b
(d) 4a2 – 3ab + a2b
Ans: (a) Length of the combined farmland (X + Y)
= (3a2 + a2b – 2ab) + (a2 + ab)
= 3a2 +a2b – 2ab + a2 + ab = 4a2 + a2b – ab = 4a2 – ab + a2b.
(3) The perimeter of the combined farmland is
(a) 8a2 + 2a2b + 4ab + 4b2
(b) 4a2 + 4ab – 2a2b – 8b2
(c) 4a2 – 2a2b + 4b2
(d) 8a2 + 2a2b – 4b2
Ans: (d) Perimeter of combined farmland (X + Y)
= 2 (length + breadth) = 2 {(4a2 – ab + a2b) + (ab – 2b2)}
= 2 {4a2 – ab + a2b + ab – 2b2} = 2 (4a2 +a2b – 2b2) = 8a2 + 2a2b – 4b2.
(4) The area of the farmland Y is
(a) a3b + a2b + ab3
(b) a3b – 2a2b2 –ab3
(c) a3b – 2a2b2 + ab3
(d) a3b – a2b2 – 2ab3
Ans: (d) Area of farmland Y = (length of farmland Y) × (breadth of farmland Y)
= (a2 + ab) (ab -2b2) = a3b – 2a2b2 + a2b2 – 2ab3
= a3b – a2b2 -2ab3.