Question

D and E are respetively to the points on the
side AB and AC of triangle ABC, such that AD=2 um
BD=3.0cm and BC = 7.5cm and DE parallel BC. The
length of DE is​

Answer 1

Answer:

3 cm

$\rule{200}2$

Given : A ∆ABC in which DE // BC. AD = 2cm, BD = 3 cm and BC = 7.5 cm.

To find : The length of DE

Solution

Since, DE // BC

→ angle ADE = angle ABC (corresponding angles)

→ angle AED = angle ACB (corresponding angles)

Hence, by AA criterion of similarity,

∆ADE ~ ∆ABC

Now, we know that ratio of corresponding sides of similar triangles are equal

→ AD/AB = DE/BC

AB = AD + DB

→ AB = 2 + 3 = 5 cm

So,

2/5 = DE/7.5

→ DE = 2/5 × 7.5

→ DE = 2 × 1.5

→ DE = 3 cm.

Hence, the length of side DE is 3 cm.

Answer 2

Answer:

The length of side DE is 3 cm.

Step-by-step explanation:

Given Information -

• ∆ABC in which DE ║ BC.
• AD = 2cm.
• BD = 3 cm.
• BC = 7.5 cm.

To Find -

The  length of DE.

Solution -

As Given,

DE ║ BC.

So,

There are 2 corresponding angles now,

They are,

⇒ ∠ADE = ∠ABC.

⇒ ∠AED = ∠ACB.

Now,

As we know -

AA triangle of similarity.

Statement -

Two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional.

∴ ∆ADE ~ ∆ABC

Now,

⇒ $\dfrac{AD}{AB}=\dfrac{DE}{BC}$

⇒ AB = AD + DB

⇒ AB = 2 + 3 = 5 cm.

⇒ $\dfrac{2}{5}=\dfrac{DE}{7.5}$

⇒ DE = $\dfrac{2}{5}$ × 7.5

⇒ DE = 2 × 1.5

⇒ DE = 3 cm.

Hence, The length of DE is 3cm.