Question

In the given figure. If DE|| BC Find EC.​

Answer 1

Step-by-step explanation:

Given: DE||BC

To find: EC

Solution:

DA/DB = AE/EC [B.P.T.]

1.5/3 = 1/EC

[By Cross Multiplication]

(1.5)EC = 3

EC = 3/ 1.5

EC = 3 x 10/15

EC = 2

Therefore, EC = 2 cm

Answer 2

Given: The figure.

To find: The value of EC.

Solution:

In the given figure, the triangles ABC and ADE have the ∠A common. Since BC and DE are parallel to one another, the angles ∠E and ∠C are equal. Also, angles ∠D and ∠B are equal. This is because these are corresponding angles. Thus, it can be said that the triangles ABC and ADE are similar by the AAA (Angle-Angle-Angle) postulate.

Similar triangles have the lengths of their sides in proportion. The proportion for the triangles ABC and ADE can be written as follows.

$\frac{AE}{AC} = \frac{AD}{AB} = \frac{DE}{AB}$

$\frac{1}{AC} = \frac{1.5}{4.5}$

$AC = 3$

Since the values of AC and AE are known, the value of EC can be calculated.

$EC = AC - AE$

      $= 3-1$

      $= 2 cm$

Therefore, the value of EC is 2 cm.