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

Question

Construct a triangle XYZ in which &#x2220; Y = 30&#xB0;, &#x2220; Z = 90&#xB0; and XY + YZ + ZX = 11 cm

Philoid · Accepted Answer

Steps of construction:

Step 1: A line segment PQ = 11cm is drawn. ( XY + YZ + ZX = 11cm)

Step 2: An angle RPQ = 30⁰is constructed at a point A and an angle SQP = 90⁰ at point B.

Step 3: Angle RPQ and SQP are bisected. The bisectors of these angles intersect each other at point X.

Step 4: Perpendicular bisectors TU of PX and WV of QX are constructed.

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

Thus, Δ XYZ is the required triangle:

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