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:
Answer & explanation
Correct answer: option 2
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.