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Question
Construct a triangle with sides 5 cm, 5.5 cm and 6.5 cm. Now construct another triangle, whose sides are \[\frac{3}{5}\] times the corresponding sides of the given triangle.
Solution
Steps of Construction
Step 1. Draw a line segment QR = 5.5 cm.
Step 2. With Q as centre and radius 5 cm, draw an arc.
Step 3. With R as centre and radius 6.5 cm, draw an arc cutting the previous arc at P.
Step 4. Join PQ and PR. Thus, ∆PQR is the required triangle.
Step 5. Below QR, draw an acute angle \[\angle\]RQX .
Step 6. Along QX, mark five points R1, R2, R3, R4 and R5 such that QR1 = R1R2 = R2R3 = R3R4 = R4R5.
Step 7. Join RR5.
Step 8. From R3, draw R3R' || RR5 meeting QR at R'.
Step 9. From R', draw P'R' || PR meeting PQ in P'.
Here, ∆P'QR' is the required triangle, each of whose sides are \[\frac{3}{5}\] times the corresponding sides of ∆PQR.
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