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

No more information.

 

Answer 1

ABC is right angle triangle and and angle B is right angle.

From the pythagoras theorem AB^2 + BC^2 = AC^2 ---> (1)

To find AC ,

First find the length of AB.

D is point on BC.

Then BD + DC = BC

9 + 4 = BC

BC = 13cm

ABD is also right angle triangle.

From the pythagoras theorem AB^2 + BD^2 = AD^2

AB^2 = AD^2 - BD^2

AB^2 = (18)^2 - (9)^2

AB = sqrt(324 - 81)

AB^2 = 243

AB = sqrt(243)

AB = 15.58

Form equation (1) AB^2 + BC^2 = AC^2

243 + 169 = AC^2

412 = AC^2

AC = sqrt(412)

AC = 20.29