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# What is the perimeter of rectangle R?

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Hussain15 wrote:
What is the perimeter of rectangle R?

(1) The area of rectangle R is 60.

(2) The length of a diagonal of rectangle R is 13.

I wanna discuss this one in detail.

Let the sides be $$x$$ and $$y$$. Question: $$P=2(x+y)=?$$

(1) $$area=xy=60$$. Clearly insufficient.
(2) $$x^2+y^2=13^2=169$$. Also insufficient.

(1)+(2) Square P --> $$P^2=4(x+y)^2=4(x^2+2xy+y^2)$$ as from (1) $$xy=60$$ and from (2) $$x^2+y^2=169$$, then $$P^2=4(x^2+2xy+y^2)=4(169+120)=4*289$$ --> $$P=\sqrt{4*289}=2*17=34$$. Sufficient.

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OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

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Hussain15 wrote:
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

What about $$13-\frac{13}{\sqrt{2}}-\frac{13}{\sqrt{2}}$$ ?
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No this is wrong. a^2+b^2 = 13^2 holds true for many values of (a,b)

You cannot deduce a and b to be 12,5

what if a^2 = 6 and b^=7, it was not even given that they have integral value. Even if it was given a and b are integers you still have to think whether any integral pair a,b exists which is unique.

no doubt 2+2 = 4, but you can not deduce 4 = 2+2 only...it can be 3+1....This reasoning will help you in CR - cause and effect.
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Hussain15 wrote:
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

Posted from my mobile device

ans c
I am no Math Genius ..but if you deduce this a^2 +b^2=C^2..then it doesn't mean that triplet a,b, c are pythgorean triplet.

But if a right angle triangle is given ..then yes a,b,c satisfy pythagoras theorem and if c is given then you can find a and b.
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Kudos for the help. Now I got this point.
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Hussain15 wrote:
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

Posted from my mobile device

Dude,

Not Every Red car is Ferrari ...

Just kidding...

So every triplet is not 13-12-5
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When can you use the x:x:x√2 ratio for triangles, i thought you could on a 90 45 45 triangle?
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Re: What is the perimeter of rectangle R? [#permalink]
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Re: What is the perimeter of rectangle R? [#permalink]
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