Question

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Answer 1

Steps of Construction:
Step 1: Draw a line segment AB = 7.6cm
Step 2: Draw a ray AX, making an acute angle ∠BAX.
Step 3: Along AX, mark (5+8 = )13points` A_1, A_2, A_3, A_4, A_5, A_6, A_7, A_8, A_9, A_10, A_11, A_12 and
 A_13` such that
`A A_1= A_1 A_2 = A_2 A_3 = A_3 A_4 = A_4 A_5 = A_6 A_7= A_8 A_9= A_9 A_10 = A_10 A_11 =  A _11A_12 =A_12 A_13` .
Step 4: Join  A₁₃ B. 
Step 5: From A₅, draw  A₅P parallel to A₁₃B ( draw an angle equal to AA₁₃ B ), meeting AB in P.

Here, P is the point on AB which divides it in the ratio 5 :8.
∴Length of AP = 2.9 cm (Approx)
Length of BP = 4.7 cm(Approx)