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. [CBSE 2014]

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.