Answer:
Steps of construction- (i) Draw \[BC=8\text{ }cm\]. (ii) Construct \[XY\], the perpendicular bisector of line segment \[BC\], meeting \[BC\]at \[M\]. (iii) Cut \[MA=4\text{ }cm\]on \[XM\]. Join \[BA\] and \[CA\], \[\Delta \text{ }ABC\] is obtained. (iv) At B, draw an acute angle in downward direction. Draw 3 arcs \[{{B}_{1}},{{B}_{2}}\] and \[{{B}_{3}}\] on it. (v) Join \[{{B}_{3}}C\] and at \[{{B}_{2}}\] draw line parallel to \[{{B}_{3}}C\], cutting \[BC\] at \[C'\]. (vi) At \[C'\] draw \[AC\] parallel to \[AC\]. (vii) \[\Delta \text{ }A'C'B\] is required triangle.
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