Draw a line segment PQ of length 7 cm. Mark a point R on it, such that l(PR) : l(RQ) = 4 : 1.

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Solution

The seg PQ of length 7 cm can be divided in the ratio 4:1 in the following way.

Steps of Construction:
1. Draw a line segment PQ of length 7 cm.
2. Now, draw a ray PL making an acute angle with PQ and draw a ray QM parallel to PL by making $∠$ PQM equal to $∠$ QPL.
3. Locate 4 points P₁, P₂, P₃, and P₄ on PL and 1 point Q₁ on QM, such that PP₁ = P₁P₂ = P₂P₃ = P₃P₄ = QQ₁.
4. Now, join P₄ Q₁ that intersects PQ at R.

So, R is the point on PQ that divides the line segment PQ in the ratio 4:1.

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Rajeev followed the following steps to construct a triangle $P Q R$ such that $P Q = 4 c m,$ $Q R = 5 c m,$ and $R P = 7 c m .$

Step 1: Draw a line segment of $Q R$ of length $5 c m .$

Step 2: Draw an arc of $4 c m$ by taking $Q$ as the centre.

Step 3: Mark the intersecting point as $P .$

Step 4: Join $Q, P$ , and $Q, R$ to get the required triangle $P Q R .$

Which of the following step is missing for constructing this triangle $P Q R ?$

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