PS - Word translation - I assume this is time consuming

[karthikpandian19]

If a rectangular swimming pool has a length of k feet, a perimeter of p feet, and an area of a square feet, which of the following must be true?


(A) k^2 - kp = 0

(B) k^2 + 2ap = 0

(C) 2(k^2) + ak + p^2 = 0

(D) 2(k^2) - p^2 = 0

(E) 2(k^2) - kp + 2a = 0


Is there any short way of solving this q?
this is really time consuming for me

[karthikpandian19]

Actually just after posting the question, i realized that this one can be easily solved by PLUGGING IN NOS. concept

Anyway , the OA will be revealed after couple of threads

[eagleeye]

This is how you could do it with algebra.

We are told that one side is k, let the other side be m.
Then we have perimeter p = 2(k+m) => m=p/2-k
Also area a = mk => m=a/k.

Equating the m in two equations:
p/2-k = a/k => pk -2k^2 =2a => 2k^2-kp+2a = 0.

Hence E

[karthikpandian19]

Thank you eagleeye

I struggled with the Algebra, as i didnt equate, as you did over here.

Anyway now the way of algebra is far more easier than Plugging here.


OA is E

This is how you could do it with algebra.

We are told that one side is k, let the other side be m.
Then we have perimeter p = 2(k+m) => m=p/2-k
Also area a = mk => m=a/k.

Equating the m in two equations:
p/2-k = a/k => pk -2k^2 =2a => 2k^2-kp+2a = 0.

Hence E