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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.

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

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

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

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Therefore, \triangle XYZ is the required triangle.

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Divya Prakash Singh

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