Practical Geome...

Length of two sides of a $$\triangle ABC$$ is $$AB=6\ cm$$ and $$BC=7\ cm$$. 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.

Length of  sides of a $$\triangle ABC$$ is $$AB=5\ cm$$, $$AC = 3\ cm$$ and $$BC=4\ cm$$. If the construction of the triangle formed by these three sides include following steps, then answer the following question: 

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the second step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass.
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle. 
5. Draw the base side $$ QR = 8\  cm $$.

For construction of a $$\triangle PQR$$, when $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the fifth step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass.
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle. 
5. Draw the base side $$ QR = 8\  cm $$.

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the first step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass .
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle. 
5. Draw the base side $$ QR = 8\  cm $$.

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the fourth step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass .
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle. 
5. Draw the base side $$ QR = 8\  cm $$.

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the third step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass. 
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle. 
5. Draw the base side $$ QR = 8\  cm $$.

Length of  sides of a $$\triangle ABC$$ is $$AB=5\ cm$$, $$AC = 3\ cm$$ and $$BC=4\ cm$$. If the construction of the triangle formed by these three sides include following steps, then answer the following question: 

Construct a right angle triangle ABC such as $$AC=5 cm ,BC=3 cm$$ , $$\angle B=90^o$$
What would be the length of $$AB$$ after construction?