Question

The perimeter of the isosceles ?ABC with the base BC is equal to 40 cm. Perimeter of the equilateral ?BCD is 45 cm. Find AB and BC.

Answer 1

Answer: AB = 12.5, BC = 15

Step-by-step explanation:

Perimeter of ΔBCD = BC + CD + BD. Since it is an isoceles triangle, then BC = CD = BD. So, Perimeter of ΔBCD = 3BC

3BC = 45

÷3      ÷3

 BC = 15

Perimeter of ΔABC = AB + BC + AC.  Since it is an isosceles triangle with BC as the base, then AB = AC. So, Perimeter of ΔABC = 2AB + BC

2AB + BC = 40

2AB + 15 = 40

         -15   -15

2AB       = 25

÷2           ÷2  

      AB  = 12.5