Question

triangle ABC is right angled at b . BD is perpendicular to AC . IF Ab = 3 cm and BC = 4 cm and AC= 5 cm . find the area of triangle ABC . Also find the length of BD

Answer 1

Step-by-step explanation:

Since, <1 + <2 = 90 deg ( given)

& <3 + <2 = 90 deg ( by angle sum property of a triangle)

=> <1 = <3

So, tri BDA ~ tri CDB ( by AA similarity criterion)

=> BD/CD = DA/DB = BA/CB ( csst )

Or, BD/x = (5-x)/BD = 3/4

=> 3x = 4BD

=> BD = 3x/4 ……………….. (1)

Since (5-x)/BD = 3/4 (csst)

So, (5-x)/(3x/4) = 3/4

=> 80 - 16x = 9x

=> 25x = 80

=> x = 80/25 = 16/5 = 3.2 cm

Since BD = 3x/4 = (3 * 3.2)/4 = 3* 0.8 = 2.4

BD = 2.4 cm