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Re: If p is the perimeter of rectangle 0, what is the value of p [#permalink]
20 Jul 2012, 03:40

3

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Expert's post

SOLUTION

If p is the perimeter of rectangle Q, what is the value of p?

Question: P=2(a+b)=?

(1) Each diagonal of rectangle Q has length 10. d^2=a^2+b^2=100. Not sufficient. (2) The area of rectangle Q is 48. ab=48. Not sufficient.

(1)+(2) Square P --> P^2=4(a^2+b^2+2ab). Now as from (1) a^2+b^2=100 and from (2) ab=48, then P^2=4(a^2+b^2+2ab)=4(100+2*48)=4*196 --> P=\sqrt{4*196}=2*14=28. Sufficient.

Re: If p is the perimeter of rectangle 0, what is the value of p [#permalink]
29 Jul 2012, 00:36

Expert's post

ctiger100 wrote:

If instead, Q were a square, would 1 be sufficient?

In a rectangle, why can't we use the Isosceles Triangle to figure out the third side since the diagonals bisect each other?

If we were told that Q is a square instead of a rectangle, then the answer would be D.

As for the second question: can you please explain what you mean? Generally you cannot find the sides of a rectangle just knowing the length of its diagonal, since knowing the length of hypotenuse (diagonal) in a right triangle (created by length and width), is not enough to find the legs of it (length and width).

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]
12 Dec 2012, 13:40

I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]
13 Dec 2012, 02:21

kelleygrad05 wrote:

I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))

Hi Kellygrad05,

There was a similar problem I was attempting yesterday on the forum.

Basically we are told that it is a rectangle but we aren't sure if the sides are Integers or not. For ex.

Diagonal-10, sides can be 6 and 8 (because of PT) or something like Square root 99 and 1...and such other combination

When you consider the st2 with above then we can figure out sides will be 6 and 8 as only in that condition Area will be 48 and Diagonal as 10.

Thanks _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]
13 Dec 2012, 03:18

1

This post received KUDOS

Expert's post

kelleygrad05 wrote:

I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))

A right triangle with hypotenuse 10, doesn't mean that we have (6, 8, 10) right triangle. If we are told that the lengths of all sides are integers, then yes: the only integer solution for right triangle with hypotenuse 10 would be (6, 8, 10).

To check this: consider the right triangle with hypotenuse 10 inscribed in circle. We know that a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

So ANY point on circumference of a circle with diameter of 10 would make the right triangle with diameter. Not necessarily sides to be 6 and 8. For example we can have isosceles right triangle, which would be 45-45-90: and the sides would be \frac{10}{\sqrt{2}}. OR if we have 30-60-90 triangle and hypotenuse is 10, sides would be 5 and 5*\sqrt{3}. Of course there could be many other combinations.

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]
13 Dec 2012, 07:37

Thank you Bunuel, it's clear my understanding of pythagorean triplets was incomplete. The example of the triangle within the circle was quite illuminating. So to summarize, if it is given that all sides of the triangle are integers, and the hypotenuse was given, only then I could have deduced it was part of a pythagorean triple, correct? Was that my only misstep at arriving at answer "A"?

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]
13 Dec 2012, 07:43

Expert's post

kelleygrad05 wrote:

Thank you Bunuel, it's clear my understanding of pythagorean triplets was incomplete. The example of the triangle within the circle was quite illuminating. So to summarize, if it is given that all sides of the triangle are integers, and the hypotenuse was given, only then I could have deduced it was part of a pythagorean triple, correct? Was that my only misstep at arriving at answer "A"?

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]
17 Dec 2013, 11:07

Bunuel wrote:

If p is the perimeter of rectangle Q, what is the value of p?

(1) Each diagonal of rectangle Q has length 10. (2) The area of rectangle Q is 48.

Diagnostic Test Question: 48 Page: 26 Difficulty: 650

1) Basically, in saying that the diagonal is 10, they are giving us the hypotenuse of a right triangle. There is no info about the two other sides though, so insufficient.

2) They are simply telling us the area, which is not enough for us to know the perimeter since there are many different products of two that can yield 48.

However, taking 1 and 2 together, they are giving us the hypothenuse (in 1) and the RELATION between the two other sides of the triangle (in statement 2). Since the pythagoran theorem restricts which size two sides can have, if we are given the third (hypothenuse), then this relation between the other two sides is enough.

Notice that I did not do any calculation at all. The DS questions are more about "does this make sense?" than they are about testing if exact boundaries and relations hold up.