A rectangular field has an area of 600 square meters. If its length were increased by 10 meters and its width decreased by 2 meters, the area of the field would remain the same. Find the original dimensions (length and width) of the field.
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Correct answer: C
Explanation
The correct answer is option 3 i.e. Length = 50 m, Width = 12 m.
Let original length = L, original width = W
L × W = 600 …(1)
(L + 10)(W – 2) = 600 ...(2)
⇒ LW – 2L + 10W – 20 = 600
⇒ 600 – 2L + 10W – 20 = 600
⇒ –2L + 10W = 20
⇒ –L + 5W = 10
From (1): L = 600/W ⇒ –600/W + 5W = 10
⇒ –600 + 5W2 = 10W
⇒ 5W2 – 10W – 600 = 0
⇒ W2 – 2W – 120 = 0
⇒ (W – 12)(W + 10) = 0
⇒ W = 12 m
⇒ L = 600/12 = 50 m
Length = 50 m and Width = 12 m