RD Sharma Solutions Chapter 11 Constructions Exercise 11.2 Class 10 Maths
Chapter Name  RD Sharma Chapter 11 Constructions 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 11.2 Solutions
1. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are (2/3) of the corresponding sides of it.
Solution
Steps of construction :
 Draw a line segment BC = 5 cm.
 With centre B and radius 4 cm and with centre C and radius 6 cm, draw arcs intersecting each other at A.
 Join AB and AC. Then ABC is the triangle.
 Draw a ray BX making an acute angle with BC and cut off 3 equal parts making BB_{1} = B_{1}B_{2}= B_{2}B_{3}.
 Join B_{3}C.
 Draw B'C' parallel to B_{3}C and C'A' parallel to CA.
2. Construct a triangle similar to a given Î”ABC such that each of its sides is (5/7)^{th }of the corresponding sides of Î”ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.
Solution
Steps of construction :
 Draw a line segment BC = 7 cm.
 Draw a ray BX making an angle of 50° and cut off BA = 5 cm.
 Join AC. Then ABC is the triangle.
 Draw a ray BY making an acute angle with BC and cut off 7 equal parts making BB = B_{1}B_{2 }= B_{2}B_{3 }= B_{3}B_{4 }=B_{4}B_{5 }= B_{5}B_{6 }= B_{6}B_{7}
 Join B_{7} and C
 Draw B_{5}C' parallel to B_{7}C and C'A' parallel to CA.
3. Construct a triangle similar to a given ∠ABC such that each of its sides is 2/3rd of the corresponding sides of Î”ABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.
Solution
Steps of construction :
 Draw a line segment BC = 6 cm.
 Draw a ray BX making an angle of 50° and CY making 60° with BC which intersect each other at A. Then ABC is the triangle.
 From B, draw another ray BZ making an acute angle below BC and intersect 3 equal parts making BB_{1} =B_{1}B_{2} = B_{2}B_{2}
 Join B_{3}C.
 From B_{2}, draw B_{2}C' parallel to B_{3}C and C'A' parallel to CA.
4. Draw a Î”ABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to Î”ABC with its sides equal to 3/4th of the corresponding sides of Î”ABC.
Solution
Steps of construction :
 Draw a line segment BC = 6 cm.
 With centre B and radius 4 cm and with centre C and radius 5 cm, draw arcs intersecting each other at A.
 Join AB and AC. Then ABC is the triangle,
 Draw a ray BX making an acute angle with BC and cut off 4 equal parts making BB_{1}= B_{1}B_{2 }= B_{2}B_{3} = B_{3}B_{4}.
 Join B_{4} and C.
 From B_{3}C draw C_{3}C' parallel to B_{4}C and from C', draw C'A' parallel to CA.
5. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.
Solution
Steps of construction :
 Draw a line segment BC = 5 cm.
 With centre B and radius 6 cm and with centre C and radius 7 cm, draw arcs intersecting each other at A.
 Join AB and AC. Then ABC is the triangle.
 Draw a ray BX making an acute angle with BC and cut off 7 equal parts making BB_{1} = B_{1}B_{2} = B_{2}B_{3} = B_{3}B_{4} = B_{4}B_{5} = B_{5}B_{6} = B_{6}B_{7}.
 Join B_{5} and C.
 From B_{7}, draw B_{7}C' parallel to B_{5}C and C'A' parallel CA.
6. Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to Î”ABC with its sides equal to (5/4)th of the corresponding sides of Î”ABC.
Solution
Steps of construction :
 Draw a line segment AB = 4.5 cm.
 At A, draw a ray AX perpendicular to AB and cut off AC = AB = 4.5 cm.
 Join BC. Then ABC is the triangle.
 Draw a ray AY making an acute angle with AB and cut off 5 equal parts making AA_{1} = A_{1}A_{2} = A_{2}A_{3} =A_{3}A_{4} = A_{4}A_{5}
 Join A_{4} and B.
 From A_{5}, draw A_{5}B' parallel to A_{4}B and B'C' parallel to BC.
7. Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5 cm and 4 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.
Solution
Steps of construction :
 Draw a line segment BC = 5 cm.
 At B, draw perpendicular BX and cut off BA = 4 cm.
 Join AC, then ABC is the triangle
 Draw a ray BY making an acute angle with BC, and cut off 5 equal parts making BB_{1} = B_{1}B_{2} = B_{2}B_{3} = B_{3}B_{4} = B_{4}B_{5}
 Join B_{3} and C.
 From B_{5}, draw B_{5}C' parallel to B_{3}C and C'A' parallel to CA.
8. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.
Solution
Steps of construction :
 Draw a line segment BC = 8 cm and draw its perpendicular bisector DX and cut off DA = 4 cm.
 Join AB and AC. Then ABC is the triangle.
 Draw a ray DY making an acute angle with OA and cut off 3 equal parts making DD_{1} = D_{1}D_{2} =D_{2}D_{3} = D_{3}D_{4}
 Join D_{2}
 Draw D_{3}A' parallel to D_{2}A and A'B' parallel to AB meeting BC at C' and B' respectively.
9. Draw a Î”ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are (3/4)th of the corresponding sides of the Î”ABC.
Solution
Steps of construction :
 Draw a line segment BC = 6 cm.
 At B, draw a ray BX making an angle of 60° with BC and cut off BA = 5 cm.
 Join AC. Then ABC is the triangle.
 Draw a ray BY making an acute angle with BC and cut off 4 equal parts making BB_{1}= B_{1}B_{2} B_{2}B_{3}=B_{3}B_{4}.
 Join B_{4} and C.
 From B_{3}, draw B_{3}C' parallel to B_{4}C and C'A' parallel to CA.
10. Construct a triangle similar to Î”ABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.
Solution
Steps of construction :
 Draw a line segment AB = 4.6 cm.
 At A, draw a ray AX making an angle of 60°.
 With centre B and radius 5.1 cm, draw an arc intersecting AX at C.
 Join BC. Then ABC is the triangle.
 From A, draw a ray AX making an acute angle with AB and cut off 5 equal parts making AA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4 }=A_{4}A_{5}.
 Join A_{4} and B.
 From A_{5}, drawA_{5}B' parallel to A_{4}B and B'C' parallel to BC.
Solution
Steps of construction :
 Draw a triangle XYZ with some suitable data.
 Draw a ray YL making an acute angle with XZ and cut off 5 equal parts making YY_{1}= Y_{1}Y_{2} = Y_{2}Y_{3} = Y_{3}Y_{4}.
 Join Y_{4} and Z.
 From Y_{3}, draw Y_{3}Z' parallel to Y_{4}Z and Z'X' parallel to ZX.
12. Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.
Solution
 Draw right Î”ABC right angle at B and BC = 8 cm and BA = 6 cm.
 Draw a line BY making a cut angle with BC and cut off 4 equal parts.
 Join 4C and draw 3C'  4C and C'A' parallel to CA.
13. Construct a triangle with sides 5 cm, 5.5 cm and 6.5 cm. Now construct another triangle, whose sides are 3/5 times the corresponding sides of the given triangle.
Solution
Steps of construction:
 Draw a line segment BC = 5.5 cm.
 With centre B and radius 5 cm and with centre C and radius 6.5 cm, draw arcs which intersect each other at A
 Join BA and CA.
 Î”ABC is the given triangle.
 At B, draw a ray BX making an acute angle and cut off 5 equal parts from BX.
 Join C5 and draw 3D  5C which meets BC at D.
 From D, draw DE  CA which meets AB at E.
14. Construct a triangle PQR with side QR = 7 cm, PQ = 6 cm and ∠PQR = 60°. Then construct another triangle whose sides are 3/5 of the corresponding sides of Î”PQR.
Solution
Steps of construction:
 Draw a line segment QR = 7 cm.
 At Q draw a ray QX making an angle of 60° and cut of PQ = 6 cm. Join PR.
 Draw a ray QY making an acute angle and cut off 5 equal parts.
 Join 5, R and through 3, draw 3, S parallel to 5, R which meet QR at S.
 Through S, draw ST  RP meeting PQ at T.
15. Draw a Î”ABC in which base BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are 3/4 of the corresponding sides of Î”ABC.
Solution
Steps of construction:
 Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°.
 Draw a ray BX, which makes an acute angle ∠CBX below the line BC.
 Locate four points B_{1}, B_{2}, B_{3}and B_{4 }on BX such that BB_{1} = B_{1}B_{2}=B_{2}B_{3} = B_{3}B_{4}.
 Join B_{4}C and draw a line through B_{3} parallel to B_{4}C intersecting BC to C'.
 Draw a line through C' parallel to the line CA to intersect BA at A'.
16. Draw a right triangle in which the sides (other than the hypotenuse) arc of lengths 4 cm and 3 cm. Now, construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.
Solution
Steps of construction:
 Draw a right triangle ABC in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. ∠B = 90°.
 Draw a line BX, which makes an acute angle ∠CBX below the line BC.
 Locate 5 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}.
 Join B_{3} to C and draw a line through B_{5} parallel to B_{3}C, intersecting the extended line segment BC at C'.
 Draw a line through C' parallel to CA intersecting the extended line segment BA at A'.
17. Construct a Î”ABC in which AB = 5 cm, ∠B = 60°, altitude CD = 3 cm. Construct a Î”AQR similar to Î”ABC such that side of Î”AQR is 1.5 times that of the corresponding sides of Î”ACB.
Solution
Steps of construction :
 Draw a line segment AB = 5 cm.
 At A, draw a perpendicular and cut off AE = 3 cm.
 From E, draw EF  AB.
 From B, draw a ray making an angle of 60 meeting EF at C.
 Join CA. Then ABC is the triangle.
 From A, draw a ray AX making an acute angle with AB and cut off 3 equal parts making A A_{1 }= A_{1}A_{2} = A_{2}A_{3}.
 Join A_{2} and B.
 From A, draw A'B' parallel to A_{2}B and B'C' parallel to BC.