Question

in triangle abc de is parallel to bc.if ad=5cm,bd=7cm ,ac=18cm find the length of ae

Answer 1

Answer:

∴  x = 7.5 cm

Step-by-step explanation:

It is assumed that the point D lies on AB and the point E lies on AC.

Draw a figure with the given data.

Let AE = x cm

then EC = (18 - x ) cm

AD = 5 cm

BD = 7 cm

we have AE/EC = AD/BD (By basic proportionality theorem )

x / 18 - x = 5 / 7

∴ 7x = 5 (18-x)

∴  7x = 90 - 5x

∴  7x + 5x = 90

∴  12x = 90

∴  x = 90/12

∴  x = 7.5 cm

Thus, the length of AE is 7.5 cm in triangle ABC.

Answer 2

Answer:

7.5cm

Step-by-step explanation:

in triangle abc de is parallel to bc.if ad=5cm,bd=7cm ,ac=18cm find the length of ae

DE║ BC

ΔADE ≅ABC

AD/AB = AE/AC

AD = 5 cm

AB = AD + BD = 5 + 7 = 12 cm

AC = 18 cm

5/12 = AE/18

=> AE = 5 * 18/12

=> AE = 7.5cm