Question

the length of the three sides of an isosceles triangle are 5cm, 5cm and 8cm. the median is drawn from the vertex where the equal sides meet. find the length of the median

Answer 1

first match the Triangles ABC and the median BD and then then the medium will be the right angle triangle for the right angle signed and then then ABC then find out the answer

Answer 2

let ABC be an isosceles triangle and let AD be the median to the side BC.

therefore by Appoloniaus theorem we have
AB²+AC =2AD²+2BD²,

then

5²+5²=2×AD²+2×(5/2)²,

25+25=2×AD²+2×25/4,

50=2×AD²+25/2,

then

50-25/2=2×AD²,

(100-25)/2 = 2× AD²,

75/2 = 2×AD²,

hence

AD²=75/4,

AD=√(75/4),

AD=5√3/2 cm