The breadth of the given rectangle = 10 cm
Length = b + 4 = 10 + 4 = 14cm
What is the Area of a Rectangle?
Area of rectangle = length × breadth
Dimensions of the original rectangle:
Let breadth of rectangle = b
Length = b + 4
Area = b(b + 4) = b² + 4b
Dimensions of new rectangle:
Breadth = b + 3
Length = b + 4 + 3 = b + 7
Area = (b + 3)(b + 7)
Given that the area of the new rectangle would be 81 sq cm more than the area of the original rectangle, we would have the following:
(b + 3)(b + 7) = b² + 4b + 81
b² + 10b + 21 = b² + 4b + 81
Combine like terms together
b² - b² + 10b - 4b = 81 - 21
6b = 60
Divide both sides by 6
b = 10
Thus, the breadth of the given rectangle = 10 cm
Length = b + 4 = 10 + 4 = 14cm
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