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# Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm

**Solution:**

Steps of Construction:

- Draw line BC = 11
- Make angles of 30° at B and 90° at C using a protractor.
- Bisect angle B. With B as a center and any radius, draw a wide arc to intersect both the arms of angle B. With intersecting points as the center and the same radius, draw two arcs to intersect each other at P. Draw the line joining B and P and extend it beyond P.
- Bisect angle C. With C as the center and any radius, draw a wide arc to intersect both the arms of angle C. With intersecting points as the center and the same radius, draw two arcs to intersect each other at Q. Join Q and C such that it intersects ray BP at X.
- Draw perpendicular bisector of BX. With B and X as centers and radius greater than half of BX draw arcs on either side of line BX to intersect each other. Join the intersecting arcs such that the perpendicular bisector intersects BC at Y.
- Draw perpendicular bisector of CX. With C and X as centers and radius greater than half of CX draw arcs on either side of line CX to intersect each other. Join the intersecting arcs such that the perpendicular bisector intersects BC at Z.
- Join XY and XZ. XYZ is the required triangle.

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 11

**Video Solution:**

## Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm

Class 9 Maths NCERT Solutions Chapter 11 Exercise 11.2 Question 4

**Summary:**

It is given that we have to construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm. We have drawn the triangle using a compass and ruler and justified the construction.

**☛ Related Questions:**

- Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.
- Construct a triangle ABC in which BC = 8cm, ∠B = 45° and AB - AC = 3.5 cm
- Construct a triangle PQR in which QR = 6cm, Q = ∠60° and PR - PQ = 2cm.
- Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

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