The perimeter of an isosceles triangle is 36. one side is 10. what are the possible lengths of the base? find the area of the triangle.

Step-by-step explanation:

1. Length of base

There are two possibilities

(a) Base = 10

Then we have a triangle as in Fig. 1.

(b) Side = 10

Then we have a triangle as in Fig. 2.

2. Area of triangle

One way to find the area of the triangle is to use Heron's formula:

where s is the semiperimeter.

Each triangle has the same perimeter, so it also has the same semiperimeter and therefore the same area.

s = p/2 = 36/2 = 18

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