the length of a rectangle is greater than its breadth by 18 cm if both length and breadth are increased by 6 CM the area of the new rectangle form is 168 cm square more than the original rectangle find the length and breadth of the original rectangle
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Let the breadth of the rectangle be 'b' cm.
Length of the rectangle = (b + 18) cm
Area of the rectangle = b(b + 18) = b2 + 18b cm2
New breadth of the rectangle = (b + 6) cm
New length of the rectangle = (b + 24) cm
New area of the rectangle = (b + 6)(b + 24) = (b2 + 30b + 144)
⇒ (b2 + 30b + 144) = (b2 + 18b) + 168
⇒ 30b + 144 = 18b + 168
⇒ 12b = 24
⇒ b = 2
Therefore, breadth of the rectangle is 2 cm and the length is (2 + 18) = 20 cm
Length of the rectangle = (b + 18) cm
Area of the rectangle = b(b + 18) = b2 + 18b cm2
New breadth of the rectangle = (b + 6) cm
New length of the rectangle = (b + 24) cm
New area of the rectangle = (b + 6)(b + 24) = (b2 + 30b + 144)
⇒ (b2 + 30b + 144) = (b2 + 18b) + 168
⇒ 30b + 144 = 18b + 168
⇒ 12b = 24
⇒ b = 2
Therefore, breadth of the rectangle is 2 cm and the length is (2 + 18) = 20 cm
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