3-4-5 triangle

by KK Tue Sep 09, 2008 3:46 pm

Hello

I have a basic doubt about the right angled trianges. If we are given that the hypo is 5 then can be assume that in this right triangle the other two legs will be 4 and 5.

Please help me understand this concept

by **Guest** Fri Sep 12, 2008 8:40 pm

No, Please be advised that there could still be a non-integer combination of base and height whose square could equal 25. The slope of the hypotenuse may be different in that case. For ex: as we know in a 30:60:90 triangle the ration of sides is 1: sqrt 3 : 2 ; in this case if the hypotenuse is of length 5, the smallest side will be 2.5

For GMAT purposes maybe yes :) and I am assuming, that since you say hypotenuse, you are already aware that it IS a right triangle.

by **esledge** Tue Oct 28, 2008 1:28 pm

Good response, Guest, thanks!

Even if you know it is a right triangle, you will still need to know two side lengths to compute the third side, assuming you do not know the non-right angles of the triangle. Your only weapon is the Pythagorean theorem, and one equation can only help you solve for one unknown, not more.

If you know all three angles, and the triangle is one with known side ratios (e.g. 45-45-90 has sides 1:1:sqrt2 and 30-60-90 has sides 1:sqrt3:2), then you would only need to know one side length to compute the other two. Essentially, the side ratios give you two equations to determine your two unknowns.