An isosceles triangle has two sides, 5cm and 6cm. The perimeter of the triangle is 5cm______ Cm or______ cm．

An isosceles triangle has two sides, 5cm and 6cm. The perimeter of the triangle is 5cm______ Cm or______ cm．

(1) When the waist of an isosceles triangle is 5cm and the bottom is 6cm, if the sum of the two sides of the triangle is greater than the third side, then its perimeter is 5 × 2 + 6 = 16 (CM). (2) when the waist of an isosceles triangle is 6cm and the bottom is 5cm, if the sum of the two sides of the triangle is greater than the third side, then its perimeter is 6 × 2 + 5 = 17 (CM) The cases are: 16, 17

It is known that △ ABC is an isosceles triangle. If its two sides are 8 cm and 3 cm long, then its circumference is______ If its two sides are 8cm and 5cm respectively, its perimeter is______ ．

① When the waist length is 8cm, the three sides are 8cm, 8cm, 3cm, which is consistent with the trilateral relationship of the triangle. At this time, the perimeter is 19cm; when the waist length is 3cm, the three sides of the triangle are 8cm, 3cm, 3cm, because 3 + 3 < 8, which should be omitted

The radius of the circumcircle of an isosceles triangle is 5cm, and the length of its base is 8cm

Make high ad on bottom BC,
Because the radius of circumscribed circle OA = 5cm,
So ob = OC = 5cm,
Because the bottom BC = 8C = 8cm,
So DB = DC = 4cm,
So from Pythagorean theorem we can get: od = 3cm,
So the height ad = 8cm,
So waist length AB = AC = root sign (square of 8 + square of 4) = root sign 5,
Therefore, the circumference of isosceles triangle = (8 + 8 radical 5) cm