See attached image) Statement (1) ALONE is sufficient, but

Question

(See attached image)

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. 
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 
EACH statement ALONE is sufficient. 
Statements (1) and (2) TOGETHER are NOT SUFFICIENT

duttsit · Answer

D.

In a right angle triangle, altitude divides original triangle into 2 similar traingles. By similar triagle property (ratio of sides same) we can get:
2 * 2 = a * b

knowing a or b will give the other and we can find a + b.

ellisje22 · Answer

Thanks for your help...but I'm still not sure what you mean. If you take just statement 1 how can that help you find length of b? I don't follow you when you say "altitude divides into two similiar triangles"...

duttsit · Answer

https://mathworld.wolfram.com/RightTriangle.html Go down and see the section where it talks about altitude. Here are excerpts: Given a right triangle ABC, draw the altitude AH from the right angle A. Then the triangles AHC and BHA are similar. once you know similar traingles, use property: base1/base2 = perpendicular1/perpendicular2 as the two legs of the triangle are in same ratio for simiar triangles. let me know if you need more info.

andy_gr8 · Answer

D it is..
Both statements are self sufficient

There are 3 right trainsgles in the figure.

ps_dahiya · Answer

Triangle PQR will always be a right angle triangle. Two triangles made by the bisecting the main triangle are similar leading to a*b = 2* 2

So if we know value of either a or b we can find the other value. Hence we can find the value of PR

giddi77 · Answer

That's cool way of solving it duttsit! You rock!

I took a roundabout way but arrived there.

1) a =4, altitude = 2, angle = 90

SUFFICIENCY for a triangle,
All angles and 1 side known => rest of the sides can be determined
Two sides and included angle known => rest of the angles + other side can be determined

From (1), we can find angle QPR and angle angle QRP (since PQR = 90, angle inscribed in a Semi-Ole)
The smaller right angled triangle, knowing angle QRP, we are in a situation where 3 angles and one side (altitude =2) is known. Hence "b" can be found.

2) Same reasoning as #1, given b we can find a.

jinesh · Answer

Great Stuff Duttsit :-D

See attached image) Statement (1) ALONE is sufficient, but

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