Question

area and perimeter of a rectangle are a and b respectively and its length is twice the breadth if the length is doubled and the breadth is tripled area becomes a' and the perimeter p' find a' : a and p' : p​

Answer 1

Answer:

Let the Breadth of the Original Rectangle be : B

Given the Length of the Original Rectangle is Twice of it's Breadth

⇒ Length of Original Rectangle = 2 × B = 2B

We know that Area of a Rectangle = Length × Breadth

⇒ Area of the Original Rectangle = 2B × B = 2B²

Given the Area of Original Rectangle as : A

⇒ A = 2B²

We know that Perimeter of a Rectangle = 2(Length + Breadth)

⇒ Perimeter of the Original Rectangle = 2(2B + B) = 2(3B) = 6B

Given that the Perimeter of the Original Rectangle as : P

⇒ P = 6B

As some changes are made in the Length and Breadth of Original Rectangle, A New Rectangle is formed.

Given the Length of New Rectangle is Double than Original Rectangle.

⇒ Length of New Rectangle = 2 × 2B = 4B

Given the Breadth of New Rectangle is Triple than Original Rectangle

⇒ Breadth of New Rectangle = 3 × B = 3B

⇒ Area of New Rectangle (A') = 4B × 3B = 12B²

⇒ Perimeter of New Rectangle (P') = 2(4B + 3B) = 2(7B) = 14B

(a) A' : A = 12B² : 2B²

⇒ A' : A = 6 : 1

(b) P' : P = 14B : 6B

⇒ P' : P = 7 : 3