ABC is right-angled at B, and D is a point on BC. if AD = 18 cm, BD = 9 cm and CD = 4cm, find AC ?

Question

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Answer 1

from above we can know AB=sqrt(18*18-9*9)=9sqrt(3)           which sqrt(x)=x^(1/2)

then AC=sqrt(BC*BC+AB*AB)=sqrt(13*13+9*9*3)=sqrt(412)    all by using the Pythagorean Theorem.

Answer 2

First thing to do is draw the triangle with the line across it. Having the line creates another right angle triangle which enables us first to calculate AB 

AB^2 + BD^2 = AD^2 
AB^2 + 9^2 = 18 ^2 
AB^2 = 243 

By Pythagoras again you can now calculate the length of AC 

AC^2 = AB^2 + BC^2 
AC^2 = 243 + (9 + 4)^2 
AC^2 = 243 + 169 
AC = sqrt(412) 
AC = 20.28 (2dp)