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Does rectangle A have a greater perimeter than rectangle B?

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CEO
Joined: 15 Aug 2003
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Does rectangle A have a greater perimeter than rectangle B?  [#permalink]  11 Oct 2003, 09:07
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Does rectangle A have a greater perimeter than rectangle B?

(1) The length of a side of rectangle A is twice the length of a
side of rectangle B.

(2) The area of rectangle A is twice the area of rectangle B.
Intern
Joined: 16 Sep 2003
Posts: 22
Location: Buffalo (NY)
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Kudos [?]: 0 [0], given: 0

Length- La
Area -Aa

Length- Lb
Area -Ab

given

la=2lb
Aa=2Ab

lb*Bb=Ab/2lb*Ba=2Ab

gives Ba=Bb

hnec s by we need both to to give teh answer
choice ......C
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

I believe the answer should be B. Rectangle A encloses rectangle B, so perimeter of A has to be more than B
Senior Manager
Joined: 05 May 2003
Posts: 426
Location: Aus
Followers: 2

Kudos [?]: 5 [0], given: 0

anant wrote:
Length- La
Area -Aa

Length- Lb
Area -Ab

given

la=2lb
Aa=2Ab

lb*Bb=Ab/2lb*Ba=2Ab

gives Ba=Bb

hnec s by we need both to to give teh answer
choice ......C

I understand this solution. But can we not assume when the area is higher the perimeter will also be higher. If we pick numbers for length and breadth we should get B as answer.
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
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Kudos [?]: 43 [0], given: 0

Hi Geethu,

What are you saying. I tried picking numbers and I always get perimeter of A to be greater than that of B. I will try to to prove it mathematically later. Are with you answer B or not.
Intern
Joined: 08 Nov 2003
Posts: 1
Location: Houston
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[quote="anandnk"]Hi Geethu,

What are you saying. I tried picking numbers and I always get perimeter of A to be greater than that of B. I will try to to prove it mathematically later. Are with you answer B or not.[/quote]

Hey Anand,

Try 50 * 50 for A

and 1250 * 1 for B.

Area of A is 2500 and Area of B is 1250.
Perimeter of A is 200 and perimeter of B is 2502

Hence B can't be the answer.
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

Hmm. I guess I ran out of proper numbers. Good example indeed. Now I can see why C is correct.
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