question_answer

ABC is a right angled triangle, where \[\angle B=90{}^\circ .\]BD drawn perpendicular to AC. If AD = 9 cm and DC =16 cm, what is the measure of AB?

A)  15 cm

B)                     18 cm

C)  16 cm             

D)  9.5 cm   

Correct Answer: A

Solution :

\[B{{D}^{2}}=AD\times DC=9\times 16=144\] \[\therefore \]      \[BD=12\] Now,     \[A{{B}^{2}}=B{{D}^{2}}+A{{D}^{2}}\] \[=144+81=225\]      \[\therefore \]      \[AB=15\text{ cm}\]