Question

Construct a ΔPQR, in which PQ = 6 cm, QR = 7 cm and PR = 8 cm. Then, construct another triangle whose sides are `4/5` times the corresponding sides of ΔPQR.

Answer 1

Steps of Construction:
Step 1: Draw a line segment QR = 7cm.
Step 2: With Q as center and radius 6 cm, draw an arc.
Step 3: With R as center and radius 8cm, draw an arc cutting the previous arc at P
Step 4: Join PQ and PR. Thus, ΔPQR is the required triangle.
Step 5: Below QR, draw an acute angle ∠RQX.
Step 6: Along OX, mark five points `R_1,R_2,R_3,R_4 and  R_5  "such that"  QR_1 =  R_1 R_2 = R_2 R_3 = R_3 R_4 = R_4 R_5` .
Step 7: Join 5RR . 
Step 8: From  R₄, draw  R₄ R' || RR₅ meeting QR at R’.
Step 9: From R’, draw P’R’ || PRmeeting PQ in P’.

Here, ΔP'QR' is the required triangle, each of whose sides are`4/5` times the corresponding sides of ΔPQR.