The height drawn to the base of an isosceles triangle is 9 cm, and the base itself is 24 cm.
| July 24, 2021 | education
The height drawn to the base of an isosceles triangle is 9 cm, and the base itself is 24 cm. Find the radii of the inscribed in the triangle and circumscribed about the triangle
AH = CH = AC / 2 = 24/2 = 12 cm, since AH is the height and median of the ABC triangle.
The length of the hypotenuse AB is equal to: AB ^ 2 = AH ^ 2 + BH ^ 2 = 144 + 81 = 225.
AB = BC = 15 cm.
The semi-perimeter of triangle ABC is equal to:
ravs = (AB + BC + AC) / 2 = (15 + 15 + 24) / 2 = 54/2 = 27 cm.
The area of the triangle ABC is equal to: Sавс = АС * ВН / 2 = 24 * 9/2 = 108 cm2.
Also Saavs = p * r.
r = Savs / p = 108/27 = 4 cm.
R = a * b * c / 4 * Saс = 15 * 24 * 15/4 * 108 = 5400/432 = 12.5 cm.
Answer: R = 12.5 cm, r = 4 cm.
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