In the right angle ABC. BD divides the triangle ABC
into two triangles of equal perimeters. Find the
length of BD, given that AC = 100, BC = 80.
B 90º
Answers
BD = 24√5 if BD divides the triangle ABC into two triangles of equal perimeters. & AC = 100, BC = 80. ∠B = 90°
Step-by-step explanation:
AC = 100, BC = 80.
Right angle triangle at B
Applying pythagorus theorem
AC² = BC² + AB²
=> 100² = 80² + AB²
=> 10000 = 6400 + AB²
=> AB² = 3600
=> AB = 60
Let say BD = x
& AD = y => CD = 100 - y
Perimeter of Δ ABD = AB + BD + AD
= 60 + x + y
Perimeter of Δ BCD = BC + BD + CD
= 80 + x + 100 - y
60 + x + y = 80 + x + 100 - y
=> 2y = 120
=> y = 60
AD = 60 & CD = 40
now if we Drw DE ⊥ AB
=> Δ AED ≈ ΔABC
=> AE/AB = DE/BC = AD /AC
=> AE/60 = DE/80 = 60/100
=> AE = 36 & DE = 48
BE = AB - AE = 60 - 36 = 24
BD² = DE² + BE²
=> BD² = 48² + 24²
=> BD² = 2880
=> BD = 24√5
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