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densk [106]
3 years ago
5

The Length of a rectangle exceeds its breadth by 9 cm. if length and breadth are each increased by 3 cm, the area of new rectang

le will be 84 cm square more than that of the given rectangle. Find the length and breadth of given rectangle.... (A)8 cm (B)16 cm (C)9 cm (D)17 cm Note: There is no diagram Related to this question....
Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
7 0

Answer:

Breadth = 8 cm

Length = 17 cm

Step-by-step explanation:

Given rectangle:

Breadth = x cm

Length = x + 9 cm

Area = length * breadth

        = x * (x + 9)

       = x² + 9x

Rectangle with length and breadth increased:

Breadth = x + 3 cm

Length = x + 9 + 3 = x + 12 cm

Area = 84 + (x² + 9x) cm²

(x +3) * (x +12) = 84 + x² +  9x

Use FOIL method

x*x  + x*12 + 3*x + 3*12 = 84 + x² + 9x

      x² + 12x + 3x + 36  = 84 + x² + 9x  {add the like terms}

             x² + 15x  + 36  = 84 + x² + 9x

x² + 15x + 36 - 84 - x² - 9x = 0

      6x - 48 = 0

             6x = 48

             x = 48/6

        x = 8

Breadth = x = 8 cm

Length = x + 9 = 8 +9 = 17 cm

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