Question

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

Answer 1

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.