Question

Daraw a line segment of length 5.5cm, and divide it in ratio 5:8. Measure the two Parts. Write the steps of construction.​

Answer 1

Answer:

• Step1: Draw a line segment AB of length 5.6 cm
• Step2: Draw a line AC at any angle below AB
• Step3: take any distance in compass and keep the needle of the compass on point A and draw an arc intersecting the line AC. Name the intersection point as X1. Keeping the distance same in compass keep the needle on point X1 and mark an arc intersecting AC at X2. Draw 13 (5:8 given ratio 5 + 8 = 13) such parts i.e. upto X13 Step4: Join points X13 and B Now we have to divide the segment AB in ratio 5:8, i.e. 5 parts and 8 parts.
• Step5: from point, X5 draw a line parallel to BX13 intersecting AB at D, and we have divided the segment AB in ratio 5:8 And measure the length of parts, i.e. AD and DB which are 2.2 cm and 3.4 cm respectively

Answer 2

Steps of construction:

• Draw AB = 7.6 cm
• Draw ray AX, making an acute angle with AB
• Mark 13 (i.e, 5 + 8) points as A₁, A₂ ,A₁₃ on AX such that AA₁ = A₁A₂ = A₂A₃ =...A₁₂A₁₃

Join BA₁₃

Through A₅ (since we need 5 parts to 8 parts) draw CA₅ parallel to BA₁₃ where C lies on AB.

Now AC: CB = 5 : 8

By measurement, we find that AC = 2.9 cm and CB = 4.7 cm

Proof:

CA₅ is parallel to BA₁₃

By Basic Proportionality theorem, in ΔAA₁₃B

AC/BC = AA₅/A₅A₁₃ = 5/8 (By Construction)

Thus, C divides AB in the ratio 5:8.