The side of an isosceles triangle is 17 cm, and its perimeter is 50 cm. Find the area of the triangle.

| March 13, 2021 | education

1. Vertices of the triangle A, B, C. AB = BC = 17 centimeters.

2. We calculate the length of the base of the AC of a given triangle. For the calculation, we use the formula calculating the perimeter (P).

P = BC + AB + AC = 50 centimeters.

AB = 50 – 34 = 16 centimeters.

2. From the top B we draw the height of the ВC. In an isosceles triangle, according to its properties, it also performs the functions of a median, that is, it divides the AC into two identical segments AK and CК. AK = СK = 16: 2 = 8 centimeters.

3. We calculate the length of the height of the ВC:

ВK = √AB² – AK² = √17² – 8² = √289 – 64 = √225 = 15 centimeters.

4. Calculate the area (S) of a given triangle:

S = AC x ВK / 2 = 16 x 15/2 = 120 centimeters².

Answer: the area of ​​a given triangle is 120 centimeters².



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