Question

Construct a triangle PQR whose perimeter is 15 cm and whose sides are in the ratio 3:4:6.

Answer 1

The steps given below need to be followed to draw the required triangle

Step I: Draw a line segment XY of 15 cm length. (PQ + QR + RP = 15 cm)

Step II: Draw a ray XZ making an acute angle with XY such that XZ lies below XY.

Step III: Locate 13 (= 3 + 4 + 6) points on ray XY at equal distances.

Step IV: Mark points L, M and N on XZ such that XL = 3 parts, LM = 4 parts and MN = 6 parts.

Step V: Join NY. Through L and M, draw LQ|| NY and MR ||NY, intersecting XY at Q and R respectively.

Step VI: With Q as the centre and with QX as radius, draw an arc. With R as the centre and with RY as radius, draw an arc cutting the previous arc at P.

Step VII: Join PQ and PR. ΔPQR is the required triangle.