Construct a triangle XYZ in which  angleY = 30 degree, angle Z = 90 degree, xy + yz + zx = 11cm..Is it possible to  have a triangle like this without decimals considering the Pythagorean theorem??

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

The below given steps will be followed to construct the required triangle.
Step I: Draw a line segment AB of 11 cm.
(As XY + YZ + ZX = 11 cm)
Step II: Construct an angle, ∠PAB, of 30° at point A and an angle, ∠QBA, of 90° at point B.
Step III: Bisect ∠PAB and ∠QBA. Let these bisectors intersect each other at point X.
Step IV: Draw perpendicular bisector ST of AX and UV of BX.
Step V: Let ST intersect AB at Y and UV intersect AB at Z.
Join XY, XZ.
ΔXYZ is the required triangle. • 37

Step I: Draw a line segment AB of 11 cm.

(As XY + YZ + ZX = 11 cm)

Step II: Construct an angle, ∠PAB, of 30� at point A and an angle, ∠QBA, of 90� at point B.

Step III: Bisect ∠PAB and ∠QBA. Let these bisectors intersect each other at point X.

Step IV: Draw perpendicular bisector ST of AX and UV of BX.

Step V: Let ST intersect AB at Y and UV intersect AB at Z.

Join XY, XZ.

ΔXYZ is the required triangle

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How XY+YZ+ZX=AB

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diagram

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Can u answer the JUSTIFICATION for this sum . Please anybody try.... I need it...
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can u tell how to write the justification for this question
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tnq u sooo much dis helped me a lot
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tnx a lot

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Thanks a lot
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