Please please help this is my last question and if I get it wrong then I fail my test

We're not supposed to help with tests.  The police will be here shortly.

Corresponding parts of congruent triangles are congruent.  We assume the vertex letters correspond and we just write all the corresponding parts.

ΔABC ≅ ΔPQR

so ∠A ≅ ∠P  and  ∠B ≅ ∠Q  and  ∠ C≅ ∠R

and AB ≅ PQ and AC ≅ PR and BC ≅ QR

Now we go through the choices:

B, D

9514 1404 393

  x = 1 or 5

Step-by-step explanation:

The notion of "cross-multiplying" is the idea that the numerator on the left is multiplied by the denominator on the right, and the numerator on the right is multiplied by the denominator on the left. This looks like ...

Then the solution proceeds by eliminating parentheses, and solving the resulting quadratic equation.

_____

Comment on "cross multiply"

Like a lot of instructions in Algebra courses, the idea of "cross multiply" describes what the result looks like. It doesn't adequately describe how you get there. The one and only rule in solving Algebra problems is "whatever is done to one side of the equation must also be done to the other side of the equation." If you multiply one side by one thing and the other side by a different thing, you are violating this rule.

What looks like "cross multiply" is really "multiply by the product of the denominators and cancel like terms from numerator and denominator." Here's what that looks like with the intermediate steps added.