RD Sharma Solutions Class 9 Constructions Exercise 17.3

RD Sharma Class 9 Solutions Chapter 17 Ex 17.3 Free Download

RD Sharma Solutions Class 9 Chapter 17 Exercise 17.3

Q1. Construct a \(\bigtriangleup ABC\) in which BC=3.6cm, AB+AC=4.8cm and \(\angle B=60^{0}\).

 

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Steps of Construction:

 

  1. Construct a line segment BC of 3.6cm.
  2. At the point B, draw \(\angle XBC=60^{0}\).
  3. Keeping B as center and radius 4.8cm draw an arc which intersects XB at D.
  4. Join DC.
  5. Draw the perpendicular bisector of DC which intersects DB at A.
  6. Join AC.

Hence \(\bigtriangleup ABC\) is the required triangle.

 

Q2. Construct a \(\bigtriangleup ABC\) in which AB+AC=5.6cm ,BC=4.5cm and \(\angle B=45^{0}\).

 

2

 

Steps of Construction:

 

  1. Construct a line segment BC of 4.5cm.
  2. At the point B, draw \(\angle XBC=45^{0}\).
  3. Keeping B as centre and radius 5.6cm draw an arc which intersects XB at D.
  4. Join DC.
  5. Draw the perpendicular bisector of DC which intersects DB at A.
  6. Join AC.

Hence \(\bigtriangleup ABC\) is the required triangle

  

Q3. Construct a \(\bigtriangleup ABC\) in which BC=3.4cm, AB-AC=1.5cm and \(\angle B=45^{0}\).

 

3

 

Steps of Construction:

 

  1. Construct a line segment BC of 3.4cm.
  2. At the point B, draw \(\angle XBC=45^{0}\).
  3. Keeping B as centre and radius 1.5cm draw an arc which intersects XB at D.
  4. Join DC.
  5. Draw the perpendicular bisector of DC which intersects DB at A.
  6. Join AC.

Hence \(\bigtriangleup ABC\) is the required triangle.

 

Q4. Using rulers and compasses only, construct a \(\bigtriangleup ABC\), given base BC=7cm, \(\angle ABC=60^{0}\) AB+AC=12cm.

 

4

 

Steps of Construction:

 

  1. Construct a line segment BC of 7cm
  2. At the point B, draw \(\angle XBC=60^{0}\).
  3. Keeping B as center and radius 12cm draw an arc which intersects XB at D
  4. Join DC
  5. Draw the perpendicular bisector of DC which intersects DB at A
  6. Join AC

Hence \(\bigtriangleup ABC\) is the required triangle.

 

 

Q5. Construct a triangle whose perimeter is 6.4cm, and angles at the base are \(60^{0}\) \(45^{0}\).

 

5

 

Steps of Construction:

 

  1. Draw a line segment XY of 6.4cm.
  2. Draw \(\angle DXY=60^{0}\) and \(\angle EYX=45^{0}\).
  3. Draw the angle bisectors of \(\angle DXY\) and \(\angle EYX\) which intersect each other at A.
  4. Draw the perpendicular bisector of AX and AY which intersect XY at B and C respectively.
  5. Join AB and AC.

Hence \(\bigtriangleup ABC\) is the required triangle.

 

Q6. Using rulers and compasses only, construct a \(\bigtriangleup ABC\) from the following data:

 

AB+BC+CA=12cm, \(\angle B=45^{0}\) and \(\angle C=60^{0}\)

 

6

 

Steps of Construction:

 

  1. Draw a line segment XY of 12cm.
  2. Draw \(\angle DXY=45^{0}\) and \(\angle EYX=60^{0}\).
  3. Draw the angle bisectors of \(\angle DXY\) and \(\angle EYX\) which intersect each other at A.
  4. Draw the perpendicular bisector of AX and AY which intersect XY at B and C respectively.
  5. Join AB and AC.

Hence \(\bigtriangleup ABC\) is the required triangle.

 

Q7. Construct a right-angled triangle whose perimeter is equal to 10cm and one acute angle equal to \(60^{0}\).

 

7

 

Steps of Construction:

 

  1. Draw a line segment XY of 10cm.
  2. Draw \(\angle DXY=90^{0}\) and \(\angle EYX=60^{0}\).
  3. Draw the angle bisectors of \(\angle DXY\) and \(\angle EYX\) which intersect each other at A.
  4. Draw the perpendicular bisector of AX and AY which intersect XY at B and C respectively.
  5. Join AB and AC.

Hence \(\bigtriangleup ABC\) is the required triangle.

 

Q8. Construct a triangle ABC such that BC= 6cm, AB= 6cm and median AD=4cm.

 

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Steps of construction:

 

  1. Draw a line segment BC of 6cm.
  2. Take mid-point O of side BC.
  3. With center B and D and radii 6cm and 4cm, draw two arcs which intersect each other at A.
  4. Join AB, AD and AC.

Hence \(\bigtriangleup ABC\) is the required triangle.

 

Q9. Construct a right-angled triangle ABC whose base BC is 6cm and the sum of the hypotenuse AC and other side AB is 10cm.

 

9

 

Steps of Construction:

 

  1. Construct a line segment BC of 6cm.
  2. At the point B, draw \(\angle XBC=90^{0}\).
  3. Keeping B as center and radius 10cm draw an arc which intersects XB at D.
  4. Join DC.
  5. Draw the perpendicular bisector of DC which intersects DB at A.
  6. Join AC.

Hence \(\bigtriangleup ABC\) is the required triangle.

 

Q10. Construct a triangle XYZ in which \(\angle Y=30^{0}\), \(\angle Z=90^{0}\) and XY+YZ+ZX=11cm.

 

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Steps of construction:

  1. Draw a line segment AB of 11cm.
  2. Draw \(\angle DAB=30^{0}\) and \(\angle FBA=90^{0}\).
  3. Draw the angle bisectors of \(\angle DAB\) and \(\angle EBA\) which intersect each other at X.
  4. Draw the perpendicular bisector of XA and XB which intersect AB at Y and Z respectively
  5. Join XY and XZ.

Hence \(\bigtriangleup XYZ\) is the required triangle.

 

 

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