Question

If the medians of a right angled triangle that are drawn from the vertices of the acute angles are 3√3cm and 4√3cm, then the length of the hypotenuse is ____________A. 15 cm B. √15 C. 3√15 D. 2√15

Answer 1

Answer:

AD=3

CE=4

Apollonian theorem

(AB)2+(AC)2=2((AD)2+(BD)2)

b2+c2=2(9+a24)−(1)

b2+a2=2(c24+16)−(2)

b2=a2+c2

2b2+a2+c2=2(a24+c24+25)

2b2+b2=2(b24+25)

3b2=b22+50

52b2=50 b2=20

a=2113−−−√

c=43–√

Area of D=12⋅43–√⋅2113−−−√

=4311−−√.