The midline of an isosceles triangle parallel to the lateral side is 13, and the median to the base is 24

The midline of an isosceles triangle parallel to the lateral side is 13, and the median to the base is 24 Find the midline parallel to the base of the triangle

Consider a triangle ABC (AB = BC)
MK – midline parallel to the lateral side.
means BC = 2 * MK.
BC = 2 * 13 = 26.
The middle line parallel to the base is equal to half the base (AC = 2 * MN).
And since BK is the median, then it divides the base into two equal parts (KC = AK = 1/2 * AC)
Hence, MN = KC.
To find the CS, we use the Pythagorean theorem. BC ^ 2 = KC ^ 2 + BK ^ 2.
We express KC:
KC = √ (BC ^ 2 – BK ^ 2) (((√ (x) – √ x)))
Substitute the known numbers into the formula:
MN = KS = √ (26 ^ 2 – 24 ^ 2) = 10
Answer: 10