Question

please ans this question given above
it is from chapter similarity of triangles​

Answer 1

Before solving the question, let us understand the concept behind this question.

=> Similar triangle :- Triangles are similar if they have the same shape, but can be different sizes.

Properties of similar triangles:-

• Corresponding angles are congruent (same measure).
• Corresponding sides are all in the same proportion.

The concept of Basic Proportionality Theorem is used here .

Basic Proportionality Theorem :- Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally.

We know the concepts. Now, let's solve the question.

GIVEN:

• DE || BC
• Point D divides AB in ratio 3:5
• AE = 4.8 cm

TO FIND:

• Length of AC

SOLUTION:

Let EC = x

and AC = AE + EC

As DE || BC and DE is cutting ∆ABC at AB( point D ) and BC ( point E )

Therefore Basic Proportionality Theorem is applicable here ,

$\sf\mapsto{\dfrac{3}{5}=\dfrac{4.8}{x}}$

$\sf\mapsto{x=\dfrac{4.8 \times 5}{3}}$

$\sf\mapsto{x = \dfrac{24}{3}=8 \:cm}$

Now, AC = AE + EC = 4.8 + 8 = 12.8 cm

ANSWER:

$\sf\longmapsto{Length\:of\:AC\:is\:12.8\:cm}$

NOTE: For diagram, refer to attachment.

@BrainlicaLDoll