Question

Abc is a triangle in which ab=ac and d is a point on bc. If bd=5, ab=12 and ad=8 then find the length of cd?

Answer 1

The length of CD = 4$\sqrt{5}$

Step-by-step explanation:

Given data

ab = ac = 12

bd = 5 & ad = 8

From Δ A D C

$ac^{2} = ad^{2} + cd^{2}$

$cd^{2} = ac^{2} - ad^{2}$

Put the value of ac & ad in equation (1), we get

$cd^{2} = 12^{2} - 8^{2}$

$cd^{2}$ = 144 -64

$cd^{2}$ = 80

$cd = 4\sqrt{5}$

This is the length of CD.

Answer 2

Answer:

CD = 16 cm

Step-by-step explanation:

It will be done by stewart's theorem:

$BC(AD^{2} + BD.DC) = (AC^{2} . BD) + (AB^{2} . CD)$

Therefore,

let DC = x cm

(x+5)(64+5x) = (720) + (144x)

solving this you get

x=16 cm