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Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
03 Nov 2010, 15:17

2

This post received KUDOS

Expert's post

zisis wrote:

If the diagonal of rectangle Z is d, and the perimeter of rectangle Z is p, what is the area of rectangle Z, in terms of d and p? (A) (d2 – p)/3 (B) (2d2 – p)/2 (C) (p – d2)/2 (D) (12d2 – p2)/8 (E) (p2 – 4d2)/8

NO OA - once provided i will update

IMO (A)

Let the sides of rectangle be x and y.

Given: d^2=x^2+y^2 and p=2(x+y). Question: area=xy=?

Square p --> p^2=4(x^2+2xy+y^2) --> substitute x^2+y^2 by d^2 --> p^2=4(d^2+2xy) --> p^2-4d^2=8xy --> area=xy=\frac{p^2-4d^2}{8}.

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
03 Nov 2010, 15:55

Bunuel wrote:

zisis wrote:

If the diagonal of rectangle Z is d, and the perimeter of rectangle Z is p, what is the area of rectangle Z, in terms of d and p? (A) (d2 – p)/3 (B) (2d2 – p)/2 (C) (p – d2)/2 (D) (12d2 – p2)/8 (E) (p2 – 4d2)/8

NO OA - once provided i will update

IMO (A)

Let the sides of rectangle be x and y.

Given: d^2=x^2+y^2 and p=2(x+y). Question: area=xy=?

Square p --> p^2=4(x^2+2xy+y^2) --> substitute x^2+y^2 by d^2 --> p^2=4(d^2+2xy) --> p^2-4d^2=8xy --> area=xy=\frac{p^2-4d^2}{8}.

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]
03 Nov 2010, 18:47

1

This post received KUDOS

Expert's post

When answer is in terms of 1 or 2 variables, my suggestion would be to quickly take simple values. (If variables are more than that, keeping a track of their values becomes cumbersome) I would say let the sides be 3 and 4 to get diagonal, d = 5 (Pythagorean triple). Then p = 2x3 + 2x4 = 14. You are looking for an area of 3x4 = 12 Put values and check.

There is a teeny-weeny chance that two options may give you the answer you are looking for. In that case, you might have to take different values and put in those two options to pick out the winner, but the risk is worth it, in my opinion.
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Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]
09 Jan 2013, 19:58

Expert's post

Cassiss wrote:

if we take a rectangle of 2x1

area A = 2x1 = 2 perimeter P = 2x2 + 2x1 = 6 the diagonal D = sqrt(1²+2²) = sqrt(5)

for ansewer (B) (2d^2 – p)/2

(2D² - P) = 2*sqrt(5)² - 6 = 4 ==> 4/2 = 2 ==> which is the area A

the same reasoning goes for answer E

am i doing something wrong? because B and E are correct for me

When you take some numbers as you did here (say, distinct sides are 2 and 1 so p = 6, d = ...etc), it is possible that 2 or more options give you the correct answer. In that case, you need to take another set of numbers and put the values in only those two options. Hopefully, only one of them will give you the correct answer. Also, when picking numbers, try to pick those which need minimum effort. e.g. I would like to pick the sides as 3 and 4 because I know that the diagonal in that case will be 5. No messy square roots to handle.
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