Question 1206650
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This triangle has two base angle congruent, A and B, so, the triangle is isosceles.


Two angles are 45° each - hence, the third angle, C,  is  180° - 45° - 45° = 90°.


Thus the triangle is a right-angled isosceles triangle with lateral sides AC and BC.


Since AC = BC = 4 cm,  we have then  AB = {{{sqrt(4^2+4^2)}}} = {{{4*sqrt(2)}}}  (Pythagoras).


<U>ANSWER</U>.  AB = {{{4*sqrt(2)}}} = 5.656854249  (approximately).
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Solved.