Question

D and E are respectively the point on the sides of AB and AC of triangle ABC such that DE is parallel to BC and AD=3cm , DB=4cm , EC=3cm . Find AE.​

Answer 1

Answer:

search-icon-header

Search for questions & chapters

search-icon-image

Class 10

>>Maths

>>Triangles

>>Basic Proportionality Theorem (Thales Theorem)

>>In ABC, D and E are points...

Question

Bookmark

In △ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.

Medium

Solution

verified

Verified by Toppr

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

AB

AD

=

AC

AE

=

BC

DE

⇒

AB

AD

=

AC

AE

⇒

15

6

=

AC

8

⇒6AC=15×8

⇒6AC=120

⇒AC=

6

120

=20