Question

In the figure, D and E are the points of sides AB and AC of

triangle ABC

such that DE parallel to

BC. If
B= 30

and

A =40

find x, y, z. ​

Answer 1

Answer:

Given D and E are point on sides AB and AC respectively of triangle ABC such that Area(ΔDBC) = Area(ΔEBC).

Given that Area(ΔDBC) = Area(ΔEBC).

Then the height of triangle DBC and Triangle EBC are the same because both triangles are the same

Then it possible that both triangle on the same base and between parallel line BC and DE

Therefore, they will lie between the same parallel lines.

∴BC∥DE [henceproved

Answer 2

Answer:

ANSWER

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that AD=4x−38, BD=3x−1, AE=8x−7 and CE=5x−3. Let AC=x

Using the basic proportionality theorem, we have

BD

AD

=

AC

AE

⇒

3x−1

4x−3

=

x

8x−5

⇒x(4x−3)=(3x−1)(8x−5)

⇒4x

2

−3x=3x(8x−5)−1(8x−5)

⇒4x

2

−3x=24x

2

−15x−8x+5

⇒4x

2

−3x=24x

2

−23x+5

⇒24x

2

−23x+5−4x

2

+3x=0

⇒20x

2

−20x+5=0

⇒5(4x

2

−4x+1)=0

⇒4x

2

−4x+1=0

⇒(2x)

2

−(2×2x×1)x+1

2

=0(∵(a−b)

2

=a

2

+b

2

−2ab)

⇒(2x−1)

2

=0

⇒(2x−1)=0

⇒2x=1

⇒x=

2

1

Hence, x=

2

1

.