In triangle ABC, points D and E are on the sides of BC and AC respectivelysuch that B-D-C, A-E-C and DE | AB. If CE = 4 cm, AE = 5cm and BD = 4.5 cm, then BC = ..............
Answers
Answer:
In triangle ABC, points D and E are on the sides of BC and AC & DE ║ AB. If CE = 4 cm, AE = 5cm and BD = 4.5 cm, then BC = 8.1 cm
Step-by-step explanation:
in Δ ABC & Δ DCE
DE║ AB
so Δ ABC ≅ Δ DCE
AB/DE = AC/CE = BC/DC
CE = 4 cm AE = 5cm
AC = AE + CE = 9 cm
BD = 4.5 cm DC = BC - BD = BC - 4.5 cm
9/4 = BC/(BC - 4.5)
=> 9BC - 40.5 = 4BC
=> 5BC = 40.5 cm
=> BC = 8.1 cm
Answer:
8.1 cm
Step-by-step explanation:
Using property of triangle: A line segment joining any two points on two sides of triangle and parallel to third side divides the two sides in same ratio.
Thus from the figure, we can write:
AE/EC = BD/DC
From the question: CE = 4 cm
AE= 5 cm
BD = 4.5 cm
Substituting the values:
5/4 = 4.5/DC
⇒ DC = 3.6 cm
Now, BC = BD + DC
= 4.5 cm + 3.6 cm
= 8.1 cm
