Question

in ABC DE||BC DE = 3cm BC 9cm &AD 2cm what is the length of AB​

Answer 1

Answer:

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Answer 2

Given: DE || BC, DE = 3cm, BC = 9cm, AD 2cm

To find: The length of AB​

Solution: Since DE || BC, angle D = angle B and angle E = angle C.

Angle A remains the same.

Now the AAA (angle-angle-angle) similarity theorem states that two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

So by AAA criteria, we see that triangle ABC ∼ triangle ADE.

Since  DE/BC = 3 cm/9 cm

          ⇒ DE/BC = 1/3

          ⇒ AD/AB = 1/3

          ⇒ AB = 3AD

          ⇒ AB = 3 × 2 cm

           ⇒ AB = 6 cm

Answer: 6 cm