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. 

Answer 1

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.