In an isosceles triangle ABC, angle B is obtuse, BD height is 8cm. Find the perimeter of triangle ABC if the perimeter of triangle ABD is 24cm.
In an isosceles triangle, the sides are equal:
AB = BC.
The height of an isosceles triangle extending from an obtuse angle to the base divides it in half:
AD = DC = AC / 2.
The perimeter of a triangle is the sum of all its sides:
P = AB + BC + AC.
Since the length of the AC side is equal to the sum of the segments AD and DC, and the AB side of these triangles is common, the perimeter of the ABC triangle will be equal to the doubled sum of the AB and AD sides:
P = (AB + AD) 2.
To do this, we find the sum of the segments AB and AD. Since the perimeter of the triangle ABD is 24 cm, and the side BD is 8 cm, then:
AB + AD = 24 – 8 = 16 cm.
P = 16 * 2 = 32 cm.
Answer: The perimeter of triangle ABC is 32 cm.
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