Question

in triangle ABC D AND E ARE POINTS ON THE SIDE AB AND AC RESPECTIVELY , SUCH THAT DE || BC AND AD:DB =4:3 IF AE = 6CM FIND CE​

Answer 1

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=6 cm, DB=9 cm and AE=8 cm.

Using the basic proportionality theorem, we have

$\frac{ad}{ab} = \frac{ae}{ac} = \frac{de}{bc}$

$\frac{ad}{ab} = \frac{ae}{ac}$

$\frac{6}{15} = \frac{8}{ac}$

$6ac = 15 \times 8$

$6ac = 120$

hence ac=20cm