Question 60

Triangle ABC is right angled at B and D is a point of BC such that BD = 5 cm, AD = 13 cm and AC = 37 cm. then find the length of DC in cm.

Solution

From right angled triangle ABD,

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

13$$^2$$ = AB$$^2$$ + 5$$^2$$

169 = AB$$^2$$ + 25

AB$$^2$$ = 144

AB = 12 cm

From right angled triangle ABC,

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

37$$^2$$ = 12$$^2$$ + BC$$^2$$

1369 = 144 + BC$$^2$$

BC$$^2$$ = 1225

BC = 35

BD + DC = 35

5 + DC = 35

DC = 30 cm

Hence, the correct answer is Option B


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