Question

ABC is isosceles with AB=AC=8 units and BC=6 units. D and E are midpoints of AB and BC respectively. Calculate the length of DE?

Answer 1

The triangle is drawn and is shown in the image attached with.

We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same. 

D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:

AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units

So,

$4 :x = 8 : 6 \\ \\ \frac{4}{x} = \frac{8}{6} \\ \\ x=4* \frac{6}{8}=3$

Therefore, the length of DE will be 3 units