QB: Geometry Triangles 2

[contact.sumeshn]

What is the length of segment BC?

(1) Angle ABC is 90 degrees.

(2) The area of the triangle is 30.

Link to the diagram:
http://www.postimage.org/image.php?v=TsLAY4A

Pls provide a detailed explanation as to why Stmt 2 is insufficient.

[gayathri248]

With statement 2, you can determine BC only if you assume Angle ABC is 90 degrees. If you don't know angle ABC, BC will not be perpendicular to AB and hence can't be the height (height can be determined by statement2 since it gives the area)

[tim]

If the area is to be 30, considering 13 as the base the height has to be 60/13, or a little less than 5. Mentally remove segment BC from the drawing, and you'll see that AB is free to swing around point A. We can get different heights depending on how we position AB, but in particular you should note that there are two positions we can place AB that will give us a height of 60/13 - one produces an acute angle at A and the other produces an obtuse angle. Thus there are exactly two distinct values BC can take on that fit the constraints of the problem..