**Constructions**

**Question 1.Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.**

**Solution:**

**Question 2.Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 23 of the corresponding sides of the first triangle.**

**Solution:**

**Question 3.Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are 75 of the corresponding sides of the first triangle.**

**Solution:**

**Question 4.Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 112 times the corresponding sides of the isosceles triangle.**

**Solution:**

**Question 5.Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 34 of the corresponding sides of the triangle ABC.**

**Solution:**

**Question 6.Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 43 times the corresponding sides of ∆ABC.**

**Solution:**

**Question 7.Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 53F times the corresponding sides of the given triangle.**

**Solution:****Steps of Construction:**1. Construct a ∆ABC, such that BC = 4 cm, CA = 3 cm and ∠BCA = 90°

2. Draw a ray BX making an acute angle with BC.

3. Mark five points B

_{1}, B

_{2}, B

_{3}, B

_{4}and B

_{5}on BX, such that BB

_{1}= B

_{1}B

_{2}= B

_{2}B

_{3}= B

_{3}B

_{4}= B

_{4}B

_{5.}

4. Join B

_{3}C.

5. Through B

_{5}, draw B

_{5}C’ parallel to B

_{3}C intersecting BC produced at C’.

6. Through C’, draw C’A’ parallel to CA intersecting AB produced at A’.

Thus, ∆A’BC’ is the required right triangle.

**Justification:**