Question

In triangle ABC, D and E are points on the sides AB and AC respectively. DE || BC,
BD = 2 cm and DE: BC = 2:3. Find AD and ratio of area of triangle ADE to the
quadrilateral BCED.​

Answer 1

Given -

• DE।।BC
• BD=2cm
• DE:BC=2:3

To find or to proof -

• Find AD
• Ratio of area of triangle

Solution :-

If you draw a line from A to E we have a triangle ADE.

Area of ADE = 18 cm^2

Let AD = 2 y

Area of ADE = (1/2)(ADxDE) =(1/2)(2y x DE) = 18

y = 18/DE

Area of ABC = 1/2((2+3)y)(AC)

=(1/2)(5(18/DE)(AC)

= 45AC/DE

But AC = (5/3) DE

Area of ABC = 45 (5/3) DE / DE

= 75 cm^2

As a check, sketch several triangles and calculate the area of ADE.