A circle is inscribed in an isosceles triangle with a side side of 15 cm and a perimeter of 54 cm. Find the radius of this circle.
| April 27, 2021 | education
Determine the length of the base of the triangle ABC. AB = Ravs – AC – BC = 54 – 15 – 15 = 24 cm.
The half-perimeter of the triangle is: p = 54/2 = 27 cm.
By Heron’s theorem, we determine the area of the triangle ABC.
Sас = √27 * (27 – 15) * (27 – 15) * (27 – 24) = √11664 = 108 cm2.
Then the radius of the inscribed circle will be equal to:
R = Savs / p = 108/27 = 4 cm.
Answer: The radius of the inscribed circle is 4 cm.
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