Math, asked by shalini683, 1 year ago

The area and the perimeter of a rectangle are A and P respectively,and its length is twice the breadth.If the length is doubled and the breadth is trebled,the area becomes A' and perimeter,P'.Find (a) A':A, and (b) P':P

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Answers

Answered by Grimmjow

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

shalini683: Answer is wrong

shalini683: In book back answer is given (a) 4:1and (b) 2:1

shalini683: check it

Grimmjow: I think my solution is correct sis. .please check the answers again.

shalini683: first clearly read question

Grimmjow: am sorry sis. .am unable get the required answer. .please report it and make it delete. .so that anyone can answer.

Answered by ishukumar70500

: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

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