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Answer :
Given: In \(\triangle{ABC}\), base BC = 12 cm, \(\angle{B}\) = \(90^\circ\) and
AB + BC = 18 cm.
Steps of construction:
1. Draw the base BC =12cm.
2. At the point B, make an \(\angle{XBC}\) = \(90^\circ\).
3. Cut a line segment BD = AB + AC = 18 cm from the ray BX.
4. Join DC.
5. Draw the perpendicular bisector PQ of CD to intersect BD at a point A.
6. Join AC.
Then, \(\triangle{ABC}\) is the required right triangle.