Question

In triangle ABC,DE//BC,AD/DB=3/5,AC=5.6 find EC

Answer 1

since de||bc           given that ad/db=3/5
ab/db=ae/ec                   ac=5.6cm ; therefore ac-ae=ec
reversing
db/ad=ec/ae
adding 1 then cross multiplying
ab+ad/ad=ec+ae/ae
ab/ad=ac/ae
8/3=5.6/ae
ae=5.6X3/8
ae=2.1 cm             therefore 5.6 - 2.1 = 3.5cm
ec=3.5cm

Answer 2

Given,

In a ∆ABC,

DE||BC

AD/DB = 3/5

AC = 5.6

To find,

The value of EC.

Solution,

We can simply solve this mathematical problem using the following process:

Geometrically, as per the "triangle proportionality theorem";

In any triangle, if a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Now, according to the question;

In the given ∆ABC,

DE||BC

=> DE is a line parallel to the side BC of the given triangle and intersects the sides AB and AC of the triangle, thus dividing these two sides in equal proportions

=> AD/DB = AE/EC {Equation-1}

Now, let us assume that EC is equal to x units.

Geometrically,

AC = AE + EC

=> 5.6 units = AE + x units

=> AE = (5.6-x) units

Now, according to the equation-1;

AD/DB = AE/EC

=> 3/5 = (5.6-x)/x

=> 3x = 5(5.6-x) = 28 - 5 x

=> 8x = 28

=> x = 3.5 units

=> EC = 3.5 units

Hence, the length of the side EC is equal to 3.5 units.