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

Q4.    Construct a triangle XYZ in which $\angle Y = 30\degree$, $\angle Z = 90\degree$° and $XY + YZ + ZX = 11 cm$.

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The steps of construction to be followed:

Step 1: For given $XY+YZ+ZX = 11 cm$, a line segment $PQ =11 cm$  is drawn.

Step 2: At points, P and Q angles of $\angle RPQ = 30^{\circ}$ and $\angle SQP =90^{\circ}$ are constructed respectively.

Step 3: Now, bisects the angle RPQ and SQP. The bisectors of these angles intersect each other at a point X.

Step 4: Construct the perpendicular bisector of PX and QX, name them as TU and WV respectively.

Step 5: Let the bisector TU intersect PQ at Y and bisector WV intersect PQ at Z. Then XY and ZY are joined.

Therefore, $\triangle XYZ$ is the required triangle.

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