# the length of a rectangle exceeds its breadth by 9 cm. if the length and breadth are each increased by 3cm the area of the new rectangle will be 84 cm2 more than that of the given rectangle . calculate the length and breadth of the given rectangle

Let x = the breadth of the rectangle

x+ 9 = the length of the rectangle

âˆ´According to the question,
(x+9+3)(x+3) = x2 + 9x + 84

The length of the rectangle = 8cm.

The breadth of the rectangle = 8+ 9=17 cm.

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Let the breadth of the orijnal rectangle be x, then the length of the orijnal rectangle will be x + 9

In the altered rectangle, the breath is increased by 3, that is x +3 and the length is also increased by 3, that is x +9 +3 = x+12

Now the new formula is,

X2 + 9X + 84 = X(X+3) + 12(X+3)

X2 + 9X + 84 = X2 +3X +12X +36

9X + 84 = 15X +36

15X - 9X = 84 -36

6X =48

X = 48 /6 = 8

This means that the breadth of the orijnal rectangle is 8 cm

The length of the orijnall rectangle is X + 9 = 8+9 =17cm

Ans: The length is 8cm and the breadth is 17cm, respectively.

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