sandeepmanocha wrote:

Bunuel wrote:

In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.

(2) The length of QR times the length of PR is equal to 12.

From Diagram it is clear that it is a Right Angled Triangle - so

1) PQ = 5, so it will become 3,4,5 Triangle, does not matter which one is 3 or 4, because what I need is Area

Area = 1/2 * 3 * 4 = 6

Now Area Using PQ as Base = 1/2*PQ*RS = 6 = > PQ.RS = 12 (Sufficient)

2) It says QR.PR = 12, which could be 3*4 or 2*6, All we know one of them is acting as the Height. So

QR.PR = 2*Area (Sufficient)

We need PQ.RS = 2 * Area, because RS is Perpendicular to PQ

so PQ*RS = QR*RS

Answer: D

Hi

sandeepmanochaJust because length of hypotenuse is 5 , the other 2 sides need not be 3 and 4 . The sides need not be a Pythagorean triple .

For example,

If PR and QR are \(\sqrt{(10)}\)and \(\sqrt{(15)}\) , then

10 + 15 = 5^2 = 25

Area = (1/2)*[ \(\sqrt{(10)}\) * \(\sqrt{(15)}\) ]

= (1/2) *\(\sqrt{(150)}\)

= (1/2) * 5 * \(\sqrt{(6)}\)

= 6.12 , which is not equal to 6

So statement 1 will not be sufficient.

Hope it helps !!

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