Triangle ABC is right angled at B and D is a point of BC such that BD…

Here, \(\Delta \)ABD is also a right angled triangle.

So,

\( { AB}^{2 } \) + \( { BD}^{2 } \) = \( { AD}^{2 } \)

= \( { AB}^{2 } \) = 169 - 25

= AB = 12

we know,

\( { AB}^{2 } \) + \( { BC}^{2 } \) = \( { AC}^{2 } \)

= \( { BC}^{2 } \) = \( { AC}^{2 } \) - \( { AB}^{2 } \)

= \( { BC}^{2 } \) = \( { 37}^{2 } \) - \( { 12}^{2 } \)

= BC = 35

= BD + DC = 35

= DC = 30

Therefore, DC is 30 cm.