If 4 cm, 8 cm, and 2 cm are the measures of three lines segment, can it be used to draw a triangle?

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Solution

The triangle is formed by three line segments 4cm, 8cm and 2cm, then it should satisfy the inequality theorem.

Hence, let us check if the sum of two sides is greater than the third side.

4 + 8 > 2 ⇒ 12 > 2 ⇒ True

8 + 2 > 4 ⇒ 10 > 4 ⇒ True

4 + 2 > 8 ⇒ 6 > 8 ⇒ False

Therefore, the sides of the triangle do not satisfy the inequality theorem. So, we cannot construct a triangle with these three line-segments.

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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 $P Q R .$

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

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