Question 66

In the given figure, if AB = 8 cm, AC = 10 cm, $$\angle$$ABD = 90$$^\circ$$ and AD = 17 cm, then the measure of CD is:

Solution

From $$\triangle$$ABC,

AB$$^2$$ + BC$$^2$$ = AC$$^2$$

$$\Rightarrow$$  8$$^2$$ + BC$$^2$$ = 10$$^2$$

$$\Rightarrow$$  64 + BC$$^2$$ = 100

$$\Rightarrow$$  BC$$^2$$ = 36

$$\Rightarrow$$  BC = 6 cm

From $$\triangle$$ABD,

$$\Rightarrow$$  AB$$^2$$ + BD$$^2$$ = AD$$^2$$

$$\Rightarrow$$  8$$^2$$ + BD$$^2$$ = 17$$^2$$

$$\Rightarrow$$  64 + BD$$^2$$ = 289

$$\Rightarrow$$  BD$$^2$$ = 225

$$\Rightarrow$$  BD = 15 cm

$$\Rightarrow$$  BC + CD = 15

$$\Rightarrow$$  6 + CD = 15

$$\Rightarrow$$  CD = 9 cm

Hence, the correct answer is Option B


Create a FREE account and get:

  • Free SSC Study Material - 18000 Questions
  • 230+ SSC previous papers with solutions PDF
  • 100+ SSC Online Tests for Free

cracku

Boost your Prep!

Download App