Question

in triangle abc, DE ll BC. If DB=5.4cm,AD=1.8cm,EC=7.2cm then find AE?​

Answer 1

Given:

In triangle ABC,

• DE║BC
• DB = 5.4 cm
• AD = 1.8 cm
• EC = 7.2 cm

To be found:

The value of AE?

Now,

[see the attached image]

We know that,

BPT - Basic Proportionality Theorem.

When a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

Another name of it is - Thales theorem.

So,

We get

$\boxed{\frac{AD}{BD}=\frac{AE}{CE}}$

So,

Putting the given values in the above, we will get,

$\implies \frac{1.8}{5.4}=\frac{AE}{7.2}$

By cross multiplication, we will get,

⇒ 7.2 * 1.8 = 5.4 * AE

⇒ 12.97 = 5.4 * AE

⇒ 12.97 ÷ 5.4 = AE

⇒ 2.4 = AE

Hence,

The value of Ae is 2.4 cm

- - -

Verification,

$\boxed{\frac{AD}{BD}=\frac{AE}{CE}}$

LHS,

$\frac{AD}{BD}= \frac{1.8}{5.4} = 0.33$

RHS,

$=\frac{AE}{CE} = \frac{2.4}{7.2} = 0.33$

Hence,

LHS = RHS (verified)

Answer 2

Given ,

In Δ ABC , DE // BC & DB = 5.4 cm , AD = 1.8 cm and EC = 7.2cm

We know that ,

Basic proportionality or Thales theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points , the other two sides are divided in the same ratio

Thus ,

$\implies \tt \frac{AD}{DB} = \frac{AE}{EC}$

$\implies \tt \frac{1.8}{5.4} = \frac{AE}{7.2}$

$\implies \tt AE = \frac{1.8 \times 7.2}{5.4}$

$\implies \tt AE = \frac{12.97}{5.4}$

$\implies \tt AE = 2.4 \: \: cm$

Hence ,

• The measure of AE is 2.4 cm