Question

In a triangle ABC, AB = 10 cm, AC = 15 cm, AD (D lies on BC) is a median and DE || AC where E is point on AB. Find AE and DE.
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Answer 1

Answer:

Given,

AB = 10 cm, AC = 15 cm, AD (D lies on BC) is a median and DE || AC where E is point on AB.

explanation:

AC || DE

therefore, DE = 1/2 AC and E would be the midpoint of AE due to mid point theorem.

therefore, DE = 15/2cm => 7.5cm and AE = 10/2 cm => 5cm

Answer 2

Given:

AB=10cm

AC=15cm

DE || AC

To find:

The length of AE and DE

Solution:

The length of AE is 5 cm and of DE is 7.5 cm.

We can find the lengths by following the given steps-

We know that if a line joining any two sides of a triangle is parallel to the third line, it passes through the mid-point of the two sides.

Since DE || AC, D is the midpoint of BC and E is the midpoint of AB, the length of DE is half the length of AC.

DE=1/2 of AC

We are given that AB=10 cm and AC=15 cm.

So, DE=1/2 of 15

=15/2

=7.5 cm

Now we will find the length of AE.

We know that E is also the midpoint of AB, so AE=1/2 of AB.

AE=1/2 of AB

=1/2 of 10

=10/2

=5 cm

Therefore, the length of AE is 5 cm and of DE is 7.5 cm.