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

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

Given:
isosceles triangle ABC,
KE – the middle line is parallel to the BC side,
KE = 13 cm,
BE – median,
BE = 24 cm.
Find the midline KР parallel to the base of the AC -?
Decision:
1) The middle line is half the parallel side. Then BC = 2 * 13 = 26 (cm);
2) Consider a right-angled triangle BEC. By the Pythagorean theorem:
BE ^ 2 + EC ^ 2 = BC ^ 2;
EC ^ 2 = BC ^ 2 – BE ^ 2;
EC ^ 2 = 26 ^ 2 – 24 ^ 2;
EC ^ 2 = 676 – 576;
EC ^ 2 = 100;
EC = 10 cm;
3) Since BE is the median, then AC = 2 EC = 2 * 10 = 20 (cm);
4) The middle line is half the parallel side. Then KP = 20: 2;
КP = 10 cm
Answer: 10 centimeters.