49In right-angled Δ ABC, BD AC.If AD 4, DC 9, then find BD

1.	49In right-angled Δ ABC, BD AC.If AD 4, DC 9, then find BD
Answer» Step-by-step explanation In triangle ABC & ADB /_ A = /_A (common) /_ABC = /_ ADB (each 90) Therefore Triangle ABC similar to Triangle ADB => AB/AD = AC/AB => AB2= AD x AC => AB2= 4 x 9 (AC=AD+CD = 4+5 = 9 cm) => AB2= 36 => AB = 6 cm In Triangle ABD using Pythagoras Theorem AB2= AD2+ BD2 62 = 42 + BD2 BD2= 36 - 16 = 20 BD = 2√5 By geometric mean. BD square=AD into DC. therefore, BD=6

Answer»

Step-by-step explanation

In triangle ABC & ADB

/_ A = /_A (common)

/_ABC = /_ ADB (each 90)

Therefore Triangle ABC similar to Triangle ADB

=> AB/AD = AC/AB

=> AB2= AD x AC

=> AB2= 4 x 9 (AC=AD+CD = 4+5 = 9 cm)

=> AB2= 36

=> AB = 6 cm

In Triangle ABD using Pythagoras Theorem

AB2= AD2+ BD2

62 = 42 + BD2

BD2= 36 - 16 = 20

BD = 2√5

By geometric mean. BD square=AD into DC. therefore, BD=6

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