In Fig.∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and C

1.	In Fig.∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.
Answer» We have, ∠ABC = 90º and BD perpendicular AC In ΔABY and ΔBDC ∠C = ∠C (Common) ∠ABC = ∠BDC(each 90º angles) then, Δ ABC ~ΔBDC (By AA Similarity) So,\(\frac{AB}{BD}\) = \(\frac{BC}{DC}\) (Corresponding parts of similar triangle area proportion) Or \(\frac{5.7}{3.8}\) = \(\frac{BC}{5.4}\) Or BC = 5.7/3.8 x 8.1 Or BC = 12.15 cm

In Fig.∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Answer»

We have,

∠ABC = 90º and BD perpendicular AC

In ΔABY and ΔBDC

∠C = ∠C (Common)

∠ABC = ∠BDC(each 90º angles)

then, Δ ABC ~ΔBDC (By AA Similarity)

So,\(\frac{AB}{BD}\) = \(\frac{BC}{DC}\) (Corresponding parts of similar triangle area proportion)

Or \(\frac{5.7}{3.8}\) = \(\frac{BC}{5.4}\)

Or BC = 5.7/3.8 x 8.1

Or BC = 12.15 cm