Question

5
In AABC, DE||BC, if AD=x, DB = 2x, AE = 3x, EC = x+10, AB is​

Answer 1

Answer:

x=4

Step-by-step explanation:

In Δ ABC, DE ∥ BC

∴

DB

AD

=

EC

AE

(By basic proportionality theorem)

⇒

x−2

x

=

x−1

x+2

⇒x(x−1)=(x+2)(x−2)

⇒x

2

−x=x

2

−4

⇒x=4.

Answer 2

Given:

• DE || BC
• AD = x
• DB = 2x
• AE = 3x
• EC = x + 10

To find:

→ AB = ?

Method:

The concept of Basic Proportionality Theorem or Thales Theorem is used here.

It states that → If a line is parallel to a side of a triangle, then the other 2 sides of the triangle are said to be intersected in the same ratio.

Applying the above theorem,

$\boxed{\sf{\dfrac{AD}{DB} = \dfrac{AE}{EC}}}$

$\\\\\Rightarrow \: \sf{\dfrac{x}{2x} = \dfrac{3x}{x+10}}$

$\\\\\rm{On\: Cross \: Multiplication,}$

$\\\\\Rightarrow \sf{2x (3x) = x(x+10)}\\\\\\\Rightarrow \sf{6x^{2} = x^{2} + 10x} \\\\\\\Rightarrow \sf{6x^{2} -x^{2} =10x}\\\\\\\Rightarrow \sf{5x^{2} =10x}\\\\\rm{Cancelling \: x \: on \: both \: sides,}\\\\\\\longrightarrow \sf{5x = 10}\\\\\\\Rightarrow \sf{x = \dfrac{10}{5}}\\\\\\\Rightarrow \boxed{\bf{x = 2}}$

Now for finding AB,

AB = AD + DB

⇒ AB = x + 2x

⇒ AB = 3x

⇒ AB = 3 × 2

∴ AB = 6 cm