Question

the length of rectangle exceeds its breadth by 14 cm if the length is decreased by 8 cm and breadth is increased by 6 and the area of both is same find the length and breadth ​

Answer 1

Given:-

• The length of rectangle exceeds its breadth by 14 cm

• if the length is decreased by 8 cm and breadth is increased by 6 and the area of both is same

To Find:-

• The Length and Breadth of Rectangle

Formulae used:-

• Area of Rectangle = L × B

Now,

Let the Breadth be "x"

→ Length of Rectangle = x + 14

→ Area of Original Rectangle = L × B

→Area of Original Rectangle =(x) ( x + 14) → x² + 14x

Now, Atq

→ Length of New Rectangle = x + 14 - 8→ x + 6

→ Breadth of New Rectangle = x + 6

→ Area of New Rectangle = L × B → ( x + 6) ( x + 6)

→ Area of New Rectangle = x² + 12x + 36.

But, it also given that area of both rectangle is same.

→ x² + 14x = x² + 12x + 36

→ 14x = 12x + 36

→ 14x - 12x = 36

→ 2x = 36

→ x = 36/2

→ x = 18

Therefore,

→ Breadth of Original Rectangle = 18cm

→ Length of Original Rectangle = x + 14→ 32

Hence, The length and Breadth of Rectangle is 18 and 32 respectively.