Question

(iv) AC-= 4 AB-. 21. In the given figure line BD is parallel to CE. AB = 1.5 cm, BC = 6 cm, AD = 2 cm. Find DE N 6 cm (ii) 8 cm (in) 4 cm (iv) cannot be found. 22. Check the relation between the following triangles:​

Answer 1

Answer:

Step-by-step explanation:AB/BC=AD/DE=1.5/6=2/DE

DE=12/1.5=8cm

Answer 2

Length of the side DB is (ii) 8 cm.

Given:

AB = 1.5 cm

BC = 6 cm

AD = 2 cm

To find:

length of DE

Solution:

• According to Basic proportionality theorem or Thales theorem, a line which is running parallel to any one side of a triangle that further intersects other two  sides of the same triangle then, the sides of the triangle are divided in the same ratio.

According to the question, line DB runs parallel to the side CE of ΔACE.

Hence, applying Basic proportionality theorem, we get

$\frac{AB}{BC}= \frac{AD}{DE}$

Substituting the given vales in the equation, we get

$\frac{1.5}{6}= \frac{2}{DE}$

$\frac{1}{4}= \frac{2}{DE}$

$DE=8cm$

Final answer:

Hence, the length of side DE is (ii) 8 cm