The perimeter of the isosceles δabc with the base bc is equal to 40 cm. perimeter of the equilateral △bcd is 45 cm. find ab and bc.

The side lengths of an equilateral triangle are all the same, so each of the 3 sides is 1/3 of the total perimeter of the triangle. Here, that means ...

... BC = (1/3)×(45 cm) = 15 cm

The side lengths of an isosceles triangle are the same. Added to the base length, they give the perimeter.

... AB + AB + BC = 40 cm

... 2×AB + 15 cm = 40 cm . . . substitute the value of BC

... 2×AB = 25 cm . . . . . . . . . . subtract 15 cm

... AB = (25 cm)/2 = 12.5 cm

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