Please anyone solve this question
The length of a rectangle exceeds its breadth by 9cm. If the length and breadth are each increased by 3cm, the area of new rectangle will be 84cm ^2 more than original rectangle. Find the length and breadth of the original rectangle.
Answers
Let the breadth of the rectangle is x cm.
Given that length of a rectangle exceeds its breadth by 9 cm.
Thus, the length of the rectangle = x + 9 cm.
So, the original dimensions are x and x + 9.
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Given that length and breadth increased by 3 cm.
length = x + 3.
Breadth = x + 12.
So, the new dimensions are x + 3 and x + 12
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Given that Area of new rectangle will be 84cm^2 more than original rectangle.
= > x(x + 9) + 84 = (x + 3)(x + 12)
= > x^2 + 9x + 84 = x^2 + 12x + 3x + 36
= > x^2 + 9x + 84 = x^2 + 15x + 36
= > 9x + 84 = 15x + 36
= > x = 8.
So,
Breadth of the original rectangle = 8 cm.
Length of the original rectangle = 17 cm.
Hope this helps!