Question

In right angled triangle ABC,BD is perpendicular to AC.If AD=4 ,DC=9,then find BD​

Answer 1

Answer:

6cm

Step-by-step explanation:

Given In right angled triangle triangle ABC, BD perpendicular AC if AD= 4, DC =9 then find BD​

In a right angled triangle ABC, A is common, angle ABC = angle ADB

BD is perpendicular to AC.

ABC is similar to ADB

AB / AD = AC / AB

AB ^2 = AD x AC (because AC = AD + CD = 4 + 9 = 13 cm)

AB^2 = 4 x 13

AB^2 = 52

AB = √52

AB = 2√13 cm

AB^2 = AD^2 + BD^2

(2√13)^2 = 4^2 + BD^2

16 + BD^2 = 52

BD^2 = 52 - 16

BD^2 = 36

BD = 6 cm

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Answer 2

Answer:

BD = 6

Step-by-step explanation:

• By using theorem of geometric mean,
• BD² = AD × DC
• BD² = 4 ×9
• BD² = 36
• BD = 6

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