Question

Draw a line segment of length 7.6 cm and divide It Into a ratio of 5 : 8. Measure both the parts.

Answer 1

Given :

Line segment AB = 7.6 cm.

Construction : (1) In circle of ∆ABC.

Steps of Construction:

(1) Draw a line segment AB = 7.6 cm

(2) Draw a ray AX making an acute angle with
AB at A.

(3) Locate 5 + 8 = 13 points A₁, A₂, A₃,………A₁₃ at equal distance on AX. Join A₁₃B.

(4) From point A₅ draw a line AA₅P || AA₁₃B to meet AB at P. 

i.e., ∠BA₁₃A = ∠PA₅A.

Then AP : PB = 5 : 8

Hence, AP and PB are the requires parts of AB.

Proof : In ∆AA₅P and ∆AA₁₃B,

A₁₃B || A₅P

∴ by BPT, we get

\(\frac { { AA }_{ 5 } }{ { A }_{ 5 }{ A }_{ 13 } } \) = \(\frac { AP }{ PB }\)

But \(\frac { { AA }_{ 5 } }{ { A }_{ 5 }{ A }_{ 13 } } \) = \(\frac { 5 }{ 8 }\) (By construction)

∴ \(\frac { AP }{ PB }\) = \(\frac { 5 }{ 8 }\)

Hence, point P, divides AB into the ratio 5 : 8.

Measuring two parts, we get.

AP = 2.9 cm

and PB = 4.7 cm