Question

In the ∆ABC, D and E are points on side AB and AC respectively such that

DE II BC. If AE=2cm, AD=3cm and BD=4.5cm, then find CE.​

Answer 1

Answer:

CE = 1 cm

Step-by-step explanation:

by basic proportionality theorem,

AD/AB = AE/AC

3/4.5 = 2/ AC

3AC = 9

AC = 3

AC - AE = CE

CE = 1 CM

Answer 2

Given:

∆ABC has points

1. D on the side AB
2. E on the side AC

• DE II BC
• AE = 2cm
• AD = 3cm
• BD = 4.5cm

To Find:

CE

Solution:

• We can say that the lines AB and AC intersect at one point. Therefore, the proportionality theorem can be used to find the length of an unknown section in the triangle.
• The proportionality theorem suggests that any section on a side of the triangle has the same ratio with any section on the other side of the triangle.

For this case the relationship looks like:

$\frac{CE}{AE} = \frac{BD}{AD}$

$\frac{CE}{2} = \frac{4.5}{3} \\\\CE = \frac{4.5}{3} * 2\\\CE= 3$

Hence, the length of CE is 3cm.

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