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

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Solution

The steps to draw the triangle of given measurement is as follows:

Draw a line segment AB which is equal to XY + YZ + ZX = 11 cm.

Make an angle ∠Y = 30° from point A and the angle be ∠LAB

Make an angle ∠Z = 90° from point B and the angle be ∠MAB

Bisect ∠LAB and ∠MAB at point X.

Now take the perpendicular bisector of the line XA and XB and the intersection point be Y and Z respectively.

Join XY and XZ

Therefore, XYZ is the required triangle.

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