Final answer:
The value of x in the congruent triangles CDE and FGE, where side GE equals 42, is also 42. For other mathematical problems, methods like setting up proportions or using the quadratic equation may be applied to find x.
Step-by-step explanation:
The question requires us to find the value of x in a triangle congruence scenario. Given that triangle CDE is congruent to triangle FGE and side GE equals 42, we can deduce that if x corresponds to GE in triangle CDE, then x also equals 42.
To solve other problems where the value of x is not given directly, we can use similar triangles, proportions, or the quadratic equations as suggested by the provided information. For example, by setting up a proportion such as 1.5 inches/10 feet = 42 inches/x feet and cross-multiplying, or by evaluating the quadratic equation where x equals approximately 0.00139. These methods are fundamental in figuring yourself how to solve geometry and algebra problems.