# Class 9 RD Sharma Solutions – Chapter 17 Constructions- Exercise 17.3

Last Updated : 13 Dec, 2022

### Question 1. Construct a Î” ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and âˆ B = 60Â°.

Solution:

Steps of Construction:

1. Draw a line segment BC = 8.6cm.

2. Draw âˆ B = 60Â°.

3. Now, with centre B and radius = 4.8cm, draw an arc that intersects line XB at point D.

4. Join DC.

5. Now, draw a perpendicular of DC that intersects DB at point A.

6. Join AC.

So, Î” ABC is the triangle.

### Question 2. Construct a Î” ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and âˆ B = 45Â°.

Solution:

Steps of Construction:

1. Draw a line segment BC = 4.5cm.

2. Draw âˆ B = 45Â°.

3. Now, with centre B and radius = 5.6cm, draw an arc that intersect line BC at point O.

4. Join DC.

5. Now, draw the perpendicular bisector of DC that intersect line BC at point A.

6.Join AC.

So, Î” ABC is the triangle.

### Question 3. Construct a Î” ABC in which BC = 3.4 cm, AB âˆ’ AC = 1.5 cm and âˆ B = 45Â°.

Solution:

Steps of Construction:

1. Draw  a line segment BC = 3.4cm.

2. Draw âˆ B = 45Â°.

3. Now, with centre B and radius = 1.5cm, draw an arc that intersect line BX at point D.

4. Join DC.

5. Now, draw a perpendicular bisector of DC that intersects line BX at point A.

6. Join AC.

So, Î” ABC is the triangle.

### Question 4. Using ruler and compasses only, construct a Î”ABC, given base BC = 7 cm, âˆ ABC = 60Â° and AB + AC = 12 cm.

Solution:

Steps of Construction:

1. Draw a line segment BC = 7cm.

2. Draw âˆ B = 60Â°

3. Now, with centre B and radius = 12cm, draw an arc that intersects line BX at point D.

4. Join DC.

5. Now, draw the perpendicular bisector of DC that intersects line BD at point A.

6. Join AC.

So, Î” ABC is the triangle.

### Question 5. Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60Â° and 45Â°.

Solution:

Steps of Construction:

1. Draw a line segment XY = 6.4cm.

2. Draw the angle bisectors ofâˆ EYY = 45Â°

3. Now, draw the angle bisector ofâˆ BXY and âˆ EYX that intersect each other at point A.

4. Draw the perpendicular bisector of lines AX and AY that intersect line XY at points B and C.

5. Join AB and AC.

So, Î” ABC is the triangle.

### AB + BC + CA = 12 cm, âˆ B = 45Â° and âˆ C = 60Â°.

Solution:

Steps of Construction:

1. Draw a line segment XY = 12cm.

2. Drawâˆ X = âˆ B = 45Â° and âˆ Y = âˆ C = 60Â°

3. Now, draw the angle bisectors of angles of DXY and EYX that intersects each other at point A.

4. Draw the perpendicular bisector of AX and AY that intersect line XY at points B and C.

5. Join AB and AC.

So, Î” ABC is the triangle.

### Question 7. Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to 60Â°.

Solution:

Steps of Construction:

1. Draw a line segment XY = 10cm.

2. Draw âˆ X = âˆ B = 90 and âˆ Y = âˆ C = 60

3. Now, draw the angle bisector of âˆ DXY and âˆ EXY that intersect each other at point A.

4. Draw the perpendicular bisectors of AX and AY which intersects line XY at points B and C.

5. Join AB and AC.

So, Î” ABC is the triangle.

### Question 8. Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm.

Solution:

Steps of Construction:

1. Draw a line segment BC = 6 cm

2. Now, take mid-point D of line BC.

3. With centre B and D and radius 6cm and 4cm, draw two arcs that intersects each other at point A.

4. Now, join AB, AD, and AC.

So, Î” ABC is the triangle.

### Question 9. Construct a right triangle ABC whose base BC is 6 cm and the sum of hypotenuse AC and other side AB is 10 cm.

Solution:

Steps of Construction:

1. Draw a line segment BC = 6cm.

2. Now, at point B draw and angle of 90Â°

3. Now, with centre B and radius = 10cm, draw an arc that intersect line XB at point D.

4. Join DC.

5. Draw the perpendicular bisector of DC that intersects line DB at point A.

6. Join AC.

So, Î” ABC is the triangle.

### Question 10. Construct a triangle XYZ in which âˆ Y = 30Â°, âˆ Z = 90Â° and XY + YZ + ZX = 11.

Solution:

Steps of Construction:

1. Draw a line segment AB = 11cm.

2. Draw âˆ A =âˆ Y = 30 and âˆ B = âˆ Z = 90

3. Now, draw the angle bisectors of âˆ DAB and âˆ EBA that intersect each other at point X.

4. Draw the perpendicular bisectors of XA and XB that intersect line AB at points Y and Z.

5. Join XY and XZ.

So, Î” XYZ is the triangle.

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