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प्रश्न
∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `"PQ"/"LT" = 3/4`.
उत्तर
Analysis:
|
Rough Figure |
As shown in fig, let the points R, P, L and RQT be collinear.
∆PQR ~ ∆LTR ...[Given]
∴ ∠PRQ ≅ ∠LRT … [Corresponding angles of similar triangles]
`"PR"/"LR" = "QR"/"TR" = "PQ"/"LT" = 3/4`.
∴ sides of ∆LTR are longer than corresponding sides of ∆PQR.
∴ the length of side QR will be equal to 3 parts out of 4 equal parts of side TR.
So, if we construct ∆PQR, point T will be on side RQ, at a distance equal to 4 parts form R.
Now, point L is the point of intersection of ray RP and a line through T, parallel to PQ.
∆LTR is the required triangle similar to ∆PQR.
Steps of Construction:
- Draw ∆PQR such that PQ = 4.2 cm, QR = 5.4 cm and PR = 4.8 cm, choosing QR = 5.4 cm as base.
- Draw ray RS making an acute angle with side RQ.
- Taking convenient distance on the compass, mark 4 points R1, R2, R3, and R4, such that RR1 = R1R2 = R2R3 = R3R4.
- Join R3Q. Draw line parallel to R3Q through R4 to intersects ray RQ at T.
- Draw a line parallel to side PQ through T. Name the point of intersection of this line and ray RP as L.
- ∆LTR is the required triangle similar to ∆PQR.
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