Final answer:
In an isosceles triangle with equal sides AB and BC, the length of side AC (denoted as 'y') can be found using the Pythagorean theorem.
Step-by-step explanation:
In an isosceles triangle, two sides are equal in length. Let's call the length of each equal side 'x'. So, AB = BC = x.
Using the Pythagorean theorem, we know that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Since ABC is isosceles, we can consider either AB or BC as the base and use the Pythagorean theorem to find the length of the altitude, which is represented by side AC. Let's use AB as the base and AC as the altitude.
Let's say AC = y. Applying the Pythagorean theorem to triangle ABC, we have:
x^2 + (0.5y)^2 = y^2
Simplifying the equation, we get:
x^2 + 0.25y^2 = y^2
0.75y^2 = x^2
y^2 = x^2 / 0.75
y = sqrt(x^2 / 0.75)
So, the length of side AC (y) is equal to the square root of x squared divided by 0.75.