Question

In triangle ABC, if BC=3rd, AC=5cm, and D is the midpoint of AB.angle B =90°.find the value of DC?
Plz give an detail answer with explanation! !

Answer 1

AC = 5
BC = 3
using pythagoras theorem

(AB)^2 + (AC)^2 = (AC)^2
(AB)^2 + (3)^2 = (5)^2
(AB)^2 + 9 =25
(AB)^2 = 25 -9
= 16
AB = 4

Now,
AD+DB = AB

as D is the mid point on AB so,
AD = DB

AD+DB = AB
2 DB = 4
DB = 2



Now,
we got a new traingle here DBC

BC is going to be the same = 3 cm
DB = 2cm (shown above)
and angle B is still 90°

again apply the pythagoras theorem
(DB)^2 + (BC)^2 = (DC)^2
(2)^2 + (3) ^2 = (DC)^2
4 + 9 = (DC )^2
13 = (DC)^2
DC = root 13.