Question

In a triangle ABC, D and E are the points on AB and AC such that DE || BC,
iFAD = 1.5 cm, AE = 1 cm & DB = 3 cm then find EC.​

Answer 1

Answer:

EC=2cm

Step-by-step explanation:

Since DE || BC then it support basic propotionality theroem

therefore, AD/DB=AE/EC

=> 1.5/3= 1/EC

=> EC=2cm

Answer 2

Given :-

In triangle ABC

• D is point on AB

• E is point on AC

• DE || BC

• AD = 1.5 cm

• AE = 1 cm

• DB = 3 cm

To Find :-

• Length of EC

Solution :-

Given that

In triangle ABC

• D is point on AB

• E is point on AC

• DE || BC

• AD = 1.5 cm

• AE = 1 cm

• DB = 3 cm

By Basic Proportionality Theorem,

It states that, If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

So,

$\red{\rm :\longmapsto\: \bf \: \dfrac{AD}{DB} = \dfrac{AE}{EC}}$

$\rm :\longmapsto\:\dfrac{1.5}{3} = \dfrac{1}{EC}$

$\rm :\longmapsto\:\dfrac{15}{30} = \dfrac{1}{EC}$

$\rm :\longmapsto\:\dfrac{1}{2} = \dfrac{1}{EC}$

$\green{\bf\implies \:EC = 2 \: cm}$

Additional Information

1. Pythagoras Theorem :-

• This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

• This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

• This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.