Question

Given a triangle with side PQ=8 cm. To get a line PQ’=3/4 of PQ, we divide

the line segment PQ in the ratio​

Answer 1

Given that: PQ = 8cm

                   PQ' = 3/4 PQ

                          = $\frac{3}{4}$ × 8 = 6cm

Find: Ratio of the line PQ

Solution: PQ = 8cm and PQ' =6cm

               now,

               PQ = PQ' +Q'Q

             ⇒ 8 = 6 + Q'Q

             ⇒ 8 - 6 = Q'Q

             ⇒ Q'Q = 2 cm

    Thus, PQ = PQ' : Q'Q

          ⇒ PQ = 6 : 2

          ⇒ PQ = 3 : 1

Hence, PQ divides in the ratio 3 : 1.

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Answer 2

The line segment PQ is divided in the ratio 3:1.

Given:

The length of line segment PQ = 8cm.

The new point P' dived the line PQ as  PQ' = 3/4 PQ.

Explanation:

Calculate the line segment PQ'

PQ’=3/4 of PQ

PQ'= $\frac{3}{4}$×$8$

PQ = 6 cm                

AS, PQ = 8cm and PQ' =6cm

PQ = PQ' +Q'Q

8 = 6 + Q'Q

8 - 6 = Q'Q

Q'Q = 2 cm

Thus, PQ = PQ' : Q'Q

PQ = 6 : 2

PQ = 3 : 1

Thus, PQ divides the line segment in the ratio 3 : 1.

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