Final answer:
To determine the base of the isosceles triangle, one must use the Pythagorean theorem on the right triangles formed by the altitude. The base is twice the value of x, which is determined by solving the equation derived from applying the theorem. Without the specific value for x, the exact length cannot be provided.
Step-by-step explanation:
To find the length of the base in an isosceles triangle where the equal sides measure 10 inches, the altitude is x-2, and the base is 2x, we can use the Pythagorean theorem. We start by recognizing that the altitude forms two right-angled triangles within the isosceles triangle. The hypotenuse of these right triangles is one of the equal sides of the isosceles triangle, and the other two sides are half of the base and the altitude.
In this case, the altitude (x-2) and half of the base (x), along with the given side of 10 inches, can be placed into the Pythagorean theorem as follows:
(x)^2 + (x-2)^2 = 10^2
On solving this equation, we find that x equals a specific value. The base of the triangle would be 2x, which is two times our found value for x.
However, to accurately calculate this without further details, we would need more information. If we were provided with the specific value of x, we could give the exact length of the base.