Question

In triangle ABC given below, $\angle AOC={90}^{\circ }$, AO = 8 cm, BC = 9 cm and AC =10 cm. The length of AB is _______.

• A. 17 cm
• B. 15 cm
• C. 13 cm
• D. 9 cm

Answer 1

The correct option is A

17 cm

Given that, $\angle AOC={90}^{\circ },AO=8cm,BC=9cmandAC=10cm.$

In the right-angled triangle $\Delta AOC$,

$A{C}^2=A{O}^2+C{O}^2$ [By Pythagoras theorem]

$\Rightarrow {10}^2=8^2+O{C}^2$

$\Rightarrow O{C}^2=100-64$

$\Rightarrow O{C}^2=36$

$\Rightarrow OC=6cm$

Now, In the right-angled triangle $\Delta AOB$,

$A{B}^2=A{O}^2+B{O}^2$ [By Pythagoras theorem]

$\Rightarrow A{B}^2=8^2+{15}^2$ [Since $BO=BC+OC=9+6=15$]

$\Rightarrow A{B}^2=64+225$

$\Rightarrow P{R}^2=289$

$\Rightarrow PR=17cm$