Q. 144.0( 3 Votes )

The length of a rect

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
= (x2 + 4x) cm2
By the given condition, we have:
Area of the new rectangle = Area of the given rectangle + 81 cm2
\\\\ Area of the new rectangle = New length ´ New breadth
(x2 + 4x) + 81 = [(x + 4) + 3] (x + 3)
x2 + 4x + 81 = (x +7)(x +3)
x2 + 4x + 81 = x (x +3) + 7 (x + 3)
x2 + 4x + 81 = x2 + 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.

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