Final answer:
The lengths of the congruent sides of an isosceles triangle with a perimeter of 94 and involving √2 is 94√2.
Step-by-step explanation:
An isosceles triangle has two congruent sides and one different side. Let's assume that the length of the congruent sides is x and the length of the different side is y. The perimeter of the triangle is the sum of all three sides, which is x + x + y = 2x + y. Given that the perimeter is 94, we can write the equation as 2x + y = 94. Since the two congruent sides have the same length, we can also write x + x + y = 94, which simplifies to 2x + y = 94.
If √2 is involved, it means that x or y is equal to x√2 or y√2. So we can rewrite the equation as 2(x√2) + (y√2) = 94√2. Simplifying this equation, we get 2x√2 + y√2 = 94√2. Since x and y are the lengths of the sides, the answer is d) 94√2.