Answer :

Let the breadth of the rectangle be x cm.

Then the length of the rectangle will be (x + 4) cm.

Therefore, the area of the given rectangle = length ´ breadth

= (x + 4)x

= (x

By the given condition, we have:

Area of the new rectangle = Area of the given rectangle + 81 cm

\\\\ Area of the new rectangle = New length ´ New breadth

(x

x

x

x

Then the length of the rectangle will be (x + 4) cm.

Therefore, the area of the given rectangle = length ´ breadth

= (x + 4)x

= (x

^{2}+ 4x) cm^{2}By the given condition, we have:

Area of the new rectangle = Area of the given rectangle + 81 cm

^{2}\\\\ Area of the new rectangle = New length ´ New breadth

(x

^{2}+ 4x) + 81 = [(x + 4) + 3] (x + 3)x

^{2}+ 4x + 81 = (x +7)(x +3)x

^{2}+ 4x + 81 = x (x +3) + 7 (x + 3)x

^{2}+ 4x + 81 = x^{2}+ 3x + 7x + 21**Check:**

(1) (14-10)cm = 4cm, i.e. the length of rectangle exceeds the breadth by 4 cm.

(2) New length = 14 + 7 = 17 cm and new breadth = 10 + 3 = 13 cm.

Therefore, area of the new rectangle – area of the given rectangle

= 17 ´ 13 – 14 ´ 10

= 221 – 140

= 81 cm.

(1) (14-10)cm = 4cm, i.e. the length of rectangle exceeds the breadth by 4 cm.

(2) New length = 14 + 7 = 17 cm and new breadth = 10 + 3 = 13 cm.

Therefore, area of the new rectangle – area of the given rectangle

= 17 ´ 13 – 14 ´ 10

= 221 – 140

= 81 cm.

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