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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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