Geometry Question

[riteshb]

I'm struggling with this DS problem so can someone actually show how to solve the problem step by step (even though you woudn't have to on the GMAT), there's a concept that I'm not 100% sure of.

In the figure, what is the length of HK times the lenght of JL ?

(1) The length of HK is 12

(2) The length of HJ times the length of JK is equal to 48

Please click on the picture to see a rough version of the figure.

Thanks

[spiderman]

the thing that needs to be kept in mind is:
area of the traingle = 1/2 (base)*(height)
in the question we have a right angled triangle.
area = 1/2 * (HJ) * (JK) ---- > (1)
also since JL is perpendicular to HK. we can write the area in terms of HK and JL as
Area = 1/2 * (HK) * (JL) -----> (2)
from (1) and (2),
HJ * JK = HK *JL

back to the question and its options.

1) says Hk = 12. ok fine. but we still dont know what JL is. so, data given is not sufficient.
2) says HJ * JK = 48. so, from what we derived earlier. HK*JL should also be equal to 48. Hence, given data is sufficient.


hence, answer is B.

HTH !

[riteshb]

Thanks, that was a MUCH easier explanation than the Peterson's book had. I forgot that the area would be the same both ways (not using geometry in 11 years will do that)

[The Unknown]

D ( Both the statements are itself sufficient to answer ) .

Correct me if i am wrong.

Solution :

From triangle HLJ,

angle JHL = 45° = angle HJL => HL = JL.
and angle HLJ = 90 °.

From triangle JLK,

angle LJK = 45 ° = angle LKJ => LK = JL.
and angle KLJ = 90 °.

So can we say they are similar triangles ? ok .

Now :

Question: In the figure, what is the length of HK times the lenght of JL (HK x JL) ?

Given :

1. HK = 12. But HL = 1/2 Hk (coz of perpendicular bisector and similar triangles)

HL = 6. From triangle HLJ,

HL = JL, JL = 6.

Hence we can deduce (HK x JL).

2. HJ x JK = 48.

To prove this part it follows your reasoning or we can prove it an other way also.

Thanks.

[ursula]

From triangle HLJ,

angle JHL = 45° = angle HJL => HL = JL.
and angle HLJ = 90 °.

Careful, I think that's exactly the trap you're supposed to fall into - almost went for it myself...

There is nothing in the question that indicates that angle JHL is 45. It looks that way in the diagram, but DS diagrams are not drawn to scale unless that's specifically stated.

In particular, you can't assume that the line JL bisects the angle HJK - the only thing you can be sure of is that HJK is a right angle. For example, you can easily draw a 30-60-90 triangle with the right angle at HJK, and drop a vertical line from J to a point L on the hypotenuse. The length of JL in that case won't be the same as the length of JL in a 45-90-45 triangle.

[m_mkumar]

LSR...Can u answer this??

[sunil4gmat]

the asnwer should be B.

Acc to a property in geometry, in this kind of figure,

HJ * JK = HK * JL.

and no assumptions about angles can be taken.

So, Its B which is sufficient.

[lsr]

LSR...Can u answer this??

spiderman, ursula and sunil4gmat all got it right.
Answer is B.