Question

On dividing a line-segment of length 9.6 cm in the ratio 3 : 1, the length of the smaller part will be:
(A) 7.2 cm
(B) 2.4 cm
(C) 1.2 cm
(D) 3.6 cm
(B) 2.4 cm​

Answer 1

Answer:

D)3.6 cm

Answer

Open in answr app

Correct option is

3.6 cm

In △ABC we have DE∥BC

∴

BD

AD

=

EC

AE

[by basic proportionality theorem]

⇒

BD

2.4

=

4.8

3.2

⇒BD=

3.2

2.4×4.8

=3.6cm

Answer 2

Length of smaller part is 2.4 cm.

Option (B) is correct.

Given:

• A line segment of length 9.6 cm.

To find:

• On dividing a line-segment in the ratio 3 : 1, the length of the smaller part will be:
• (A) 7.2 cm
• (B) 2.4 cm
• (C) 1.2 cm
• (D) 3.6 cm

Solution:

Concept to be used:

• If line segment divided in m:n, and m>n.
• The length of smaller part $= \bf \left( \frac{n}{m + n} \right) \times \text{\bf length \: of \: line \: segment}$

Step 1:

Write the given values.

Length of line segment is 9.6 cm.

Ratio of division is 3:1.

Step 2:

Find the length of smaller part.

On comparison, we get that m=3 and n=1

So, It is clear that in 3:1, 1 is smaller.

Put the values in the formula,

Length of smaller part$= \frac{1}{4} \times 9.6$

or

$= 2.4$

Thus,

Length of smaller part is 2.4 cm.

Option (B) is correct.

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