# NCERT Solutions for Class 9 Maths Chapter 11 Constructions Ex 11.2

These NCERT Solutions for Class 9 Maths Chapter 11 Constructions Ex 11.2 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 9 Maths Chapter 11 Constructions Exercise 11.2

Question 1.
Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.
Solution:

Steps of construction:
Step-I: Draw the base BC = 7 cm and at point B make an angle say ∠XBC = 75°.
Step-II: Cut the line segment BD = AB + AC = 13 cm from die ray BX.
Step-III: Join DC and draw perpendicular bisector of DC. Which intersect DB at A.
Step-IV: Join AC.
Step-V: Triangle ABC is the required triangle.

Question 2.
Construct a triangle ABC in which BC = 8 cm, ∠B = 45° and AB – AC = 3.5 cm.
Solution:

Steps of Construction:
Step-I: Draw the base BC = 8 cm and make ∠XBC = 45°.
Step-II: Cut the Sine segment BD = AB – AC = 3.5 cm from ray BX.
Step-III: Join DC and draw the perpendicular bisector of DC.
Step-IV: Let the perpendicular bisector of DC intersect XB at A.
Step-V: Join AC.
Step-VI: Triangle ABC is the required triangle.

Question 3.
Construct a triangle PQR in which QR = 6 m, ∠Q = 60° and PR – PQ = 2 cm.
Solution:

Steps of Construction:
Step-I: Draw the base QR = 6 cm and at point Q make an angle ∠XQR = 60°.
Step-II: Cutline segment QM = PR – PQ = 2 cm from the line XQ extended on the opposite side of line segment QR.
Step-III: Join MC and draw the perpendicular bisector of MR which intersect XQ at P.
Step-IV: Join PR.
Step-V: Triangle PQR is the required triangle.

Question 4.
Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.
Solution:

Steps of Construction:
Step-I: Draw the line segment PQ = 11 cm. (= XY + YZ + ZX)
Step-II: At P construct an angle of 30° and at Q, an angle of 90°.
Step-III: Bisect these angles. Let the bisector of these angles intersect at a point X.
Step-IV: Draw perpendicular bisectors of XP and XQ which intersect PQ at Y and Z respectively.
Step-V: Join XY and XZ.
Step-VI: Triangle XYZ is the required triangle.

Question 5.
Construct a right triangle whose base is 12 cm and the sum of its hypotenuse and other side is 18 cm.
Solution:

Steps of Construction:
Step-I: Draw the base BC = 12 cm and at a point B makes an angle say ∠XBC = 90°.
Step-II: Cut the line segment BD = 18 cm (= AB + AC).
Step-III: Join DC and make a ∠DCY = ∠BDC.
Step-IV: CY intersect BX at A.
Step-V: Join AC.
Step-VI: Triangle ABC is the required triangle.

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