Question

The length of a rectangle exceeds its breadth by 9 cm. If the length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm² more than that of the given rectangle. Find the length and breadth of the given rectangle.

please show the working ​

Answer 1

Solution:

Let the l = x,

then the b = x-9

if the are increased by 3 cm then they will be:

x+3 and (x-9+3)= x-6.

then there are will be 84 sq. cm + (x*x-9)

= (x+3) (x-6) = (x*(x-9)) + 84

= x sq. - 6x + 3x - 18 = x sq. - 9x + 84

= x sq. - 3x = x sq. - 9x + 66

= -3x + 9x = 66

= 6x = 66

= x = 66/6 = 11

l = 11+3, b = 11+3-6

l = 14 and b = 8.

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Answer 2

${\huge{\mathtt{\red{AnSwEr:-}}}}$

Let the breadth of the rectangle be x meter Length of the rectangle be (x + 9) meter

Area of the rectangle length×breadth = x(x +9) m2

When length and breadth increased by 3cm then,

New length = x + 9 + 3 = x + 12 New breadth = x + 3

So, Area is (x + 12) (x + 3) = x (x + 9) + 84 x2 + 15x + 36 = x2 + 9x + 84 15x – 9x = 84 – 36 6x = 48 x = 48/6 = 8

∴ Length of the rectangle (x + 9) = (8 + 9) = 17cm and breadth of the rectangle is 8cm.

${\huge{\mathtt{\red{Thank\:You}}}}$