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Question
The perimeter of a rectangular field is 82m and its area is 400m2, find the dimension of the rectangular field.
Solution
Area of rectangular garden with sides a and b = 400 = ab
⇒ a = `400/"b"` ....(i)
Perimeter of rectangular garden with sides a and b = 82 = 2a + 2b
⇒ a + b = 41 ... (ii)
Putting (i) in (ii), we get
⇒ `400/"b" + "b" = 41`
⇒ b2 - 41b + 400 = 0
⇒ b2 - 25b - 16b + 400 = 0
⇒ b (b -25) - 16 (b - 25) = 0
⇒ (b - 25) (b - 16) = 0
⇒ b = 25 or 16.
Putting this in (i), we get, a= 16 or 25
Hence two sides of the rectangle are 16 and 25.
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