Question

In △DEF, ABǁEF such that AD=6cm, AE=18cm, and BF =24cm. Find
the length of DB.

Answer 1

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• AB║EF
• AD = 6 cm.
• AE = 18 cm.
• BF = 24 cm.

$\LARGE{\bf{\underline{\underline{TO:FIND:-}}}}$

Since AB║EF, we can use the Thales theorem:

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio. In other words:

$\mapsto \sf{\red{ \dfrac{AD}{AE} =\dfrac{DF}{BF}}}$

Substituting the given values, we get:

$\to \sf{\red{ \dfrac{6}{18} =\dfrac{DB}{24}}}$

$\sf \to DB=\dfrac{6 \times 24}{18}$

$\leadsto \boxed{\sf{\green{DB=8 \ cm.}}}$

∴DB is 8 cm.

Answer 2

Solution :-

Given,

• AD = 6CM
• AE = 18CM
• BF = 24CM
• AB || EF

Now,

• we have to find your the length of DB .
• and we can find it by using the Thales theorem .

What is thales theorem ?

• according to the thales theorem if one side of the triangle intersecting other two side of Triangle in a point then the other two sides are divided into same ratio .

So, by putting the Thales theorem we get ,

$\bold{ \blue {\: \frac{ad}{ae} = \frac{db}{</strong><strong>bf</strong><strong>} }}$

now putting the values in the formula we get ;

$= > \bold{ \red{ \frac{6}{18} = \frac{db}{24} }}$

$= > \bold{ \red{ db = \frac{6 \times 24}{18} }}$

$= > \bold{ \red{db = 8cm}}$

So, the length of the line DB is 8CM .