Advertisement Remove all ads

ΔPQR ~ ΔABC. In ΔPQR, PQ = 3.6cm, QR = 4 cm, PR = 4.2 cm. Ratio of the corresponding sides of triangle is 3 : 4, then construct ΔPQR and ΔABC - Geometry

Advertisement Remove all ads
Advertisement Remove all ads
Diagram

ΔPQR ~ ΔABC. In ΔPQR, PQ = 3.6cm, QR = 4 cm, PR = 4.2 cm. Ratio of the corresponding sides of triangle is 3 : 4, then construct ΔPQR and ΔABC

Advertisement Remove all ads

Solution


Analysis: ∆PQR ∼ ∆ABC

∴ `"PQ"/"AB" = "QR"/"BC" = "PR"/"AC"`  .....[Corresponding sides of similar triangles]

∴ `3.6/"AB" = 4/"BC" =4.2/"AC" = 3/4`   ......[Given]

∴ `3.6/"AB" = 3/4`

∴ AB = `(3.6 xx 4)/3`

∴ AB = 1.2 × 4

∴ AB = 4.8 cm 

`4/"BC" = 3/4`

∴ BC = `(4 xx 4)/3`

∴ BC = `16/3`

∴ BC = 5.3 cm (approx)

`4.2/"AC" = 3/4`

∴ AC = `(4.2 xx 4)/3`

∴ AC = 1.4 × 4

∴ AC = 5.6 cm


Steps of Construction:

  ∆PQR ∆ABC
i. Draw seg QR of 4 cm Draw seg BC of 5.3 cm
ii. Taking 3.6 cm and 4.2 cm distances on compass draw two arcs from Q and R respectively Taking 4.8 cm and 5.6 cm distance on compass draw two arcs from point B and C respectively.
iii. Name the point of intersection as P. Name the point of intersection as A.
Concept: Division of a Line Segment
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×