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 .


Given PQR and LTR are similar.
Corresponding angles will be equal.
Given PQ/LT = 3/4
PQ/LT = QR/TR = PR/LR [Corresponding sides of similar triangles]
PQ/LT= QR/TR = PR/LR = 3/4
Sides of LTR are longer than corresponding sides of PQR.
Steps of construction:
1. Draw ∆PQR such that PQ = 4.2 , QR = 5.4 , and PR = 4.8. Draw ray RS making an acute angle with side RQ.
2. Taking convenient distance on the compass, mark 4 points R1, R2, R3, and R4, such that RR1 = R1R2 = R2R3 = R3R4.
3. Join QR3. Draw a line parallel to QR3 passing through R4 to intersects ray RQ at T.
4. Draw a line parallel to side PQ through T. Name the point where parallel line intersect ray RP as L.
∆LTR is the required triangle similar to ∆PQR.

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