In the figure, DE || BC and D is the mid point of AB. Find the perimeter of triangle ABC when AE = 4.5 cm
Answers
Step-by-step explanation:
It is assumed that the point D lies on AB and the point E lies on AC.
Draw a figure with the given data.
Now increase the measure of angle B a little bit. Move the vertex A towards point D so that the length of side AC remains the same. In this process the lengths of AD and DE become smaller - however, the lengths of BD, BC and AC remain the same.
This shows that the data given is insufficient and, with the given data, you can have an infinite number of solutions.
Since DE∥BC,△ADE∼△ABC.
⇒ADAB=AEAC=DEBC
⇒ADAD+3=AE6.4=DE3.5
We can now assume a value for AD (subject to the condition that AB is not greater that AC + BC) and get the corresponding values of DE (and, if you want, AE also).
Let AD = 2 units. Then, 22+3=DE3.5⇒DE=25×3.5=1.4 units.
Let AD = 4 units. Then, 44+3=DE3.5⇒DE=47×3.5=2 units.