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gmat prep question

by jc114 » Mon May 14, 2007 7:08 am
If the length of each side of rectangle R is squared, what is the sum of the four squared lengths?
(1) the diagonal of rectangle R has length 15
(2) the product of the lengths of 2 adjacent sides of rectangle R is 108.


why is the answer A???
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by bww » Mon May 14, 2007 8:39 am
Hm...I think it's A because from I) we know the diagonal is 15, implying that the right triangle formed with two adjacent sides of the rectangle and this diagonal follows lengths of 3:4:5. Thus, its adjacent sides must be 9 and 12. We can then answer the question of the sum of four squared lengths.

You can double check this with II). It states that product of two adjacent sides is 108. Yep, 9*12=108. But with II) alone, we can't determine that the sides are 9 and 12. II) alone is not sufficient.

The answer is A.
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answer

by chris743 » Thu May 17, 2007 11:42 pm
ok, let's suppose the two lenths of the rectangle R are "a" and "b"
then, the question is " what is 2*a^2 + 2*b^2 ?

that means 2(a^2 + *b^2)

1) the lenth of the diagonal is quare root of a^+b^2

therefore, square root of 15 is a^+b^2


now you can get the value......
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by Cybermusings » Fri May 18, 2007 5:15 am
If the length of each side of rectangle R is squared, what is the sum of the four squared lengths?
(1) the diagonal of rectangle R has length 15
(2) the product of the lengths of 2 adjacent sides of rectangle R is 108.

If the two sides are x and y. then the square of the two sides = x^2 and y^2....

Statement I : If the diagonal of the rectangle = 15 then x^2 + y^2 = 15^2
(according to the pythogarous theorem)
So 2(x^2+y^2) = 2(15)^2
Thus sufficient

Statement II: The product of the 2 adjacent lengths = 108
Area = l*b = 108
it can be 54&2; 27&4; 36&3; 18&6
So insufficient

Hence A
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