In ΔABC, D and are the points on sides AB and AC, respectively such that ∠ADE = ∠B. If AD = 7 cm, BD = 5 cm and BC = 9 cm, then DE (in cm) is equal to:

5.25

In \(\Delta \)ABC and \(\Delta \)ADE

\(\angle\)ADE = \(\angle\)ABC   (Corresponding angles)

\(\angle\)AED = \(\angle\)ACB   (Corresponding angles)

So \(\Delta \)ABC and \(\Delta \)ADE are similar by AA property

AB = AD + BD

= AB = 7 + 5

= AB = 12 cm

= \(\frac{AD}{AB}\) = \(\frac{DE}{BC}\)

= \(\frac{7}{12}\) = \(\frac{DE}{9}\)

= DE = \(\frac{63}{12}\)

= DE = 5.25

Therefore, DE is 5.25.