5. In AABC, it is given that DE | BC. If AD-3 cm, DB-2 cm and DE -6 cm

1.	5. In AABC, it is given that DE \| BC. If AD-3 cm, DB-2 cm and DE -6 cm, then find BC.1
Answer» Given: ABC is a triangle , DE parallel BC and AD= 3 cm, DB=2 cm and DE=6 cm To find: AE sol: Since DE parallel BC angle ADE= angle ABC (corresponding angles) and angle AED = angle ACB Triangle ADE ≈ triangle ABC ( by AA similarity) therefore , AD/AB=DE/BC=AE/AC (1) From (1) AD/AB=AE/AC 2/5=x/18 2×18=5x 36=5x x=36/5 x=7.5cm ∵ AE = 7.5 cm

5. In AABC, it is given that DE | BC. If AD-3 cm, DB-2 cm and DE -6 cm, then find BC.1

Answer»

Given: ABC is a triangle , DE parallel BC and AD= 3 cm, DB=2 cm and DE=6 cm

To find: AE

sol: Since DE parallel BC

angle ADE= angle ABC (corresponding angles)

and angle AED = angle ACB

Triangle ADE ≈ triangle ABC ( by AA similarity)

therefore , AD/AB=DE/BC=AE/AC (1)

From (1)

AD/AB=AE/AC

2/5=x/18

2×18=5x

36=5x

x=36/5

x=7.5cm

∵ AE = 7.5 cm