Question

Length of two sides of a $△ABC$ is $AB=6cm$ and $BC=7cm$. Then, which of the following can represent the third side of the triangle ? Also, construct the triangle formed by these three sides by following these steps. Put them in proper order.

Step 1. Draw a line segment $AB=6cm$

Step 2. Now assuming $B$ as centre draw an arc of $7cm$ intersecting the previous arc at $C$.

Step 3. Assuming $A$ a centre draw an arc of radius $8cm$

Step 4. Now join $A$ to $C$ and $B$ to $C$.

• A. $8cm$, $1-3-2-4$
• B. $13cm$, $1-3-2-4$
• C. $14cm$,$1-2-3-4$
• D. $15cm$, $4-3-2-1$

Answer 1

The correct option is A $8cm$, $1-3-2-4$

A triangle can be formed if sum of any two sides is greater then the third side.

Here $AB=6$ cm and $BC=7$ cm

Now $AB+BC>AC$

$6+7>AC$

$AC<13$ cm

So only option $A$ is possibel.

Steps of construction

Step 1. Draw a line segment $AB=6cm$

Step 2. Assuming $A$ a centre draw an arc of radius $8cm$

Step 3. Now assuming $B$ as centre draw an arc of $7cm$ intersecting the previous arc at $C$.

Step 4. Now join $A$ to $C$ and $B$ to $C$.

So $1-3-2-4$ is the correct order