PLEASE FIND THE VALUE OF X

Question

Find x.

1. 
   
2. A.
3. x = 1
4. 
   
5. B.
6. x = 4
7. 
   
8. C.
9. x = 2
10. 
    
11. D.
12. There is no such x.

Answer 1

Hi Faiza A.,

At first glance, this problem would appear to be about identical triangles and their dimensions. Can you conclude that the triangles are identical? Not by S-S-A, that's not one of the three equivalence identities (A-A, S-A-S, S-S-S)!

Let's leave that for a moment, and consider: If these were identical triangles, could you solve? You have corresponding sides, that sets up two independent equations (across the two triangles, for each side type) in two variables. If you've been paying attention in your class, you know that that has either 0, 1, or an infinite number of solutions. It's quick to see algebraically that this one has 0 solutions. (x=2 for one side, x=1 for the other side, 1 ≠ 2.)

So if this problem doesn't solve algebraically, there's no point in considering anything further. But, for the future! , you should always remember to check your algebraic answer against the original problem, to make sure that it is a real solution. For an S-S-A triangle, in particular, a single triangle could have two shapes, if the angle is acute (bracketing a right triangle shape), with given values of S-S-A!

-- Cheers, --Mr. d.

Answer 2

Well, if this figure means that 5x-3=4x-1 AND 3x+1=x+3, then x=2 satisfies the problem.