Divide line segment AB measuring 7 cm in the ratio 3 : 2.

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Solution

Seg AB of length 7 cm can be divided in the ratio 3:2 in the following way.
Steps of construction:
1. Draw a line segment AB of length 7 cm.
2. Now, draw a ray AX making an acute angle with AB and draw a ray BY parallel to AX by making $∠$ ABY equal to $∠$ BAX.
3. Locate 3 points A₁, A₂ and A₃ on X and 2 points B₁ and B₂ on BY, such that AA₁ = A₁A₂ = A₂A₃ = BB₁ = B₁B₂.
4. Now, join A₃ B₂ that intersects AB at T.

So, T is the point on AB that divides the line segment AB in the ratio 3:2.

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