In an isosceles triangle CDE with base DE, the bisector CF is drawn. Find CF if the perimeter of triangle CDE is 84 cm and the perimeter of triangle CFE is 56 cm.
Perimeter of triangle CDE: P = CD + CE + DE = 84 cm;
perimeter of triangle CFE: P ‘= CE + CF + EF = 56 cm;
DE = 2 EF – the bisector drawn to the base of the isosceles triangle is the median; CD = CE – lateral sides of an isosceles triangle;
P = 2 CE + 2 EF = 2 (CE + EF); CE + EF = 1/2 P;
CF = P ‘- (CE + EF);
CF = P ‘- 1/2 P = 56 – 1/2 * 84 = 14 (cm).
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