Question

In triangle ABC, D is the mid point of AB, E is the mid point of AC. Calculate DE if BC=8cm​

Answer 1

Answer:

Refering figure,

DE=

2

1

BC

and AP=

2

1

AQ

Given, Area of ΔABC=60cm

2

or

2

1

×BC×AQ=60

or BC×AQ=120

∴ Area of ΔADE=

2

1

DE×AP

=

2

1

×

2

1

BC×

2

1

AQ=

8

1

BC×AQ

=

8

1

×120=15sq.cm.

solution

Answer 2

Answer:

3.2 cm

Step by Step Explanation:

Join DE

By mid point theorem: A line segment joining the mid points of the two sides of the triangle, is equal to half the length of the third side.

DE=BC/2

DE=8/2 =4

Mid Point Theorem explanation:

Consider, △ABC and △ADE

∠ADE=∠ABC and ∠ACB=∠AED as they are corresponding angles with lines DE∣∣BC

∠A is common.

Hence, by A.A.S. the triangles are similar

AB/AD= AC/AE = BC/DE = 2/1

Hence, DE= 2/1 BC