Question

In triangle ABC m. angleB = 90, AB = 2.5 units, BC = 6 units and Seg BD is median, Find BD.

Answer 1

Solution:
InΔABC
angle B = 90°
triangle ABC Is an right angles triangle
According to Pythagoras theorem
AB²+BC²=AC²
(2.5)²+(6)²=AC²
6.25+36=AC²
42.25=AC²
TAKING SQUARE ROOT
6.5=AC
AD = ½AC (BD IS MEDIAN)
=½*6.5
= 3.25
According to apolonius theorem
AB²+BC²= 2BD²+2AD²
(2.5)²+(6)²=2BD²+2(3.25)²
6.25+36=2BD²+2(6.5)
42.25=2BD²+13
42.25-13=2BD²
29.25=2BD²
29.25/2=BD²
14.625=BD²
TAKING SQUARE ROOT
BD=16√25