Question

The length of AB in the given figure is: (1) 8 cm (2) 6 cm (3) 4 cm (4) 10 cm​

Answer 1

Answer:

4cm

Step-by-step explanation:

construct BO parallel to CE

then find AB by BPT theorem ( Basic proportionality theorem ) also called ( Thales theorem )

Answer 2

Given: A geometric figure where the value of x is unknown

To find: The length of AB

Solution: In triangle ABC and triangle ADE,

Angle A is common.

Angle ABC = angle ADE = 90°.

Angle ACB = angle AED (as given in the figure)

Hence, triangle ABC and triangle ADE are similar by AAA criterion.

Therefore,

AB/AD = BC/DE

⇒ x/(x + 4) = 3/6

⇒ x/(x + 4) = 1/2

⇒ 2x = x + 4

⇒ 2x - x = 4

⇒ x = 4 cm

Hence, the length of AB = x = 4 cm.

Answer: Option (3) 4 cm