The ratio of the side to the base of an isosceles triangle is 5: 6, and the height of the triangle
| September 22, 2021 | education
The ratio of the side to the base of an isosceles triangle is 5: 6, and the height of the triangle to the base is 12 cm. Find the sides of the triangle.
1. Vertices of the triangle – A, B, C. AB / AC = 5/6.
2. By the condition of the problem AB: AC = 5: 6. Therefore, AC = 6AB / 5 centimeters.
3. AH = 1/2 AC, since in an isosceles triangle, the height of the BH also performs the function of the median.
AH = 3AB / 5 cm.
4. AB² = AH² + BH².
AB² = AH² + BH².
AB² = (3AB / 5) ² + 144.
25АВ² – 95АВ² / 25 = 144.
16AB² / 25 = 144.
16AB² = 25 x 144.
AB² = 25 x 9.
AB = √25 x 9 = 5 x 3 = 15 cm.
AC = 6AB / 5 = 6 x 15/5 = 18 cm.
Answer: AC = 18 cm, BC = AB = 15 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
