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.

Answer 1

Answer:

let the breadth be x

length: x+9 , breadth: x

length and breadth are incresed by 3 so,

length: x+9 +3 = x+12 ,breadth: x+3

Gn: the area of the new rectangle = 84 sq. cm

Equation:

(x+12)(x+3)= 84+ x(x+9)

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

if we transpose x2to the opposite side then it becomes x2

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

Now it becomes 15x+36 = 84 +9x

If we transpose 9x to the opposite side it becomes 15x +36 9x = 84

6x +36 = 84

6x = 84 36

6x= 48

x=48/6

x=8

length : 8+9 = 17

breadth= 8

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Answer 2

★ Given :

length of rectangle exceeds it's breadth by - 9 cm

breadth = x , length = x + 9

Area when length and breadth are increased by 3cm = 84 cm² more than the original area..

★ To find :

Length and breadth of rectangle ..

★ Solution :

Increased breadth = x+3

Increased length = (x+9)+3 = x + 12

We know that,

→ Area of rectangle = length × breadth

Original area =

x × (x+9) = x² + 9x

Increased area =

(x+3)(x+12) =

x(x+3) + 12 (x + 3)

= x² + 3x + 12x + 36

= x² + 15x + 36

According to question :

x² + 15 x + 36 is 84 greater than x² + 9x

Equation :

→ (x² + 15x + 36) - (x² + 9x) = 84

→ x² + 15x + 36 - x² - 9x = 84

→ (15x - 9x) + 36 = 84

→ 6x = 84 - 36

→ 6x = 48

→ x = 48/6

$\purple{\leadsto x = 8}$

★ Answer :

→ breadth = x = 8 cm

→ length = x + 9 = 8 + 9 = 17 cm..