Question

the length of a rectangle exceeds its breadth by 9cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84² cm more than that of the given rectangle . find the length and breadth of the given rectangle.

Answer 1

l = b+9
Given,
(l+3)(b+3) = 84 +lb

lb+ 3b+ 3l + 9 = 84 +lb
l+b = 25

Putting l = b+9

2b + 9 = 25
so b is 8...
L is 17...

Answer 2

Answer:

The length is 17 cm and the breadth is 8 cm

Step-by-step explanation:

Define x:

Let the breadth be x

The length is x + 9

Find the area in term of x:

Area = Length x Breadth

Area = x(x + 9)

Find the new dimensions:

Breadth = x + 3

Length = x + 9 + 3 = x + 12

Find the new area in term of x:

Area = Length x Breadth

Area = (x + 3)(x + 12)

Solve x:

The new area is 84 cm² more than the given area

(x + 3)(x + 12) -  x(x + 9) = 84

x² + 12x + 3x + 36 - x² - 9x = 84

6x + 36 = 84

6x = 48

x = 8

Find the dimensions:

Breadth = x = 8 cm

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

Answer: The length is 17 cm and the breadth is 8 cm