# The perimeter of an isosceles triangle ABC is 80 cm, BD is the height lowered to the base.

The perimeter of an isosceles triangle ABC is 80 cm, BD is the height lowered to the base. Perimeter of triangle ABD 52 cm.Find height BD

1. Perimeter ∆ ABC = AC + BC + AB = 80 cm.

2. Perimeter ∆ ABD = AD + AB + BD = 52 cm.

3. The height BD, drawn to the base of the isosceles triangle, also performs the functions of the median, that is, it divides the base of the AC into two equal segments:

4. BC = AB.

5. Substitute AB for BC and 2AD for AC in the first expression:

2AD + 2AB = 80 cm.

AD + AB = 40 cm. Substitute this into the second expression:

40 + BD = 52 cm.

ВD = 52 – 40 = 12 cm.

Answer: height BD is 12 cm.

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