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

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Solution

We are asked to construct a triangle XYZ such that

We will follow the following algorithm for the construction

Steps of construction-

STEP1: Draw a line segment AB of length 11 cm.

STEP2: Draw BAC = Y = and ABD =Z =

STEP3: Bisect BAC and ABD and mark the point of intersection of these angle bisectors by X.

STEP4: Draw perpendicular bisectors of AX and XB. They meet AB at point Y and Z, respectively.

STEP5: Draw XY and XZ to get the desired ΔXYZ.

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∠ Y = 30^{\circ}, ∠ Z = 90^{\circ} a n d X Y + Y Z + Z X = 11 c m

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

∠ Y

30^{0}

∠ Z

90^{0}

∠ Y = 30^{\circ}, ∠ Z = 90^{\circ} a n d X Y + Y Z + Z X = 11 c m

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