Question : Direction: A man takes 6 kms distance to go around the rectangular area. If the area of the rectangle is 2 sq. km. Find the difference between length and breadth.
Option 1: 2 km
Option 2: 0.5 km
Option 3: 1 km
Option 4: 0.75 km
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Correct Answer: 1 km
Solution : According to the question, Perimeter of the rectangular area = 6km ⇒ 2(length + breadth) = 6 ⇒ (length + breadth) = 3 km → eq. (I)
Area of the rectangle = 2 sq. km. ⇒ Length × Breadth = 2 ⇒ Length = 2/Breadth → eq. (II)
Put this in eq(I) — ⇒ (length + breadth) = 3 ⇒ 2/B + B = 3 ⇒ 2 + B² = 3B ⇒ B² – 3B +2 = 0 ⇒ B² – 2B – B +2 = 0 ⇒ B(B – 2) – 1(B – 2) = 0 ⇒ B = 1, 2
Put the value of B in eq(I) — B = 1; L + B = 3 → L + 1 = 3 → L = 2 B = 2; L + B = 3 → L + 2 = 3 → L = 1
Since length is greater than breadth. So, Length = 2km; Breadth = 1km Difference = 2 – 1 = 1km
Hence, the third option is correct.
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