Question

Construct a triangle PQR, whose perimeter is 13 cm and whose sides are in the ratio 2:3:4.

Answer 1

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

Step I: Draw a line segment XY of 13 cm length. (PQ + QR + RP = 13 cm)

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

Step III: Locate 9 (= 2 + 3 + 4) points on ray XY at equal distances.

Step IV: Mark points L, M and N on XZ such that XL = 2 parts, LM = 3 parts and MN = 4 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 the radius, draw an arc. With R as the centre and with RY as the radius, draw an arc cutting the previous arc at P.

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