In triangle ABC it is known that AB = BC, the bisector BL is 5. The area of triangle ABC is 50√2. Find the side length BC.
| February 6, 2021 | education
The bisector BL splits triangle ABC into two equal right-angled triangles ABL and LBC.
Therefore, the sides of these triangles are pairwise equal.
Because area of triangle ABC:
S = (1/2) * AC * BL = (1/2) * AC * 5 = 5 * AC / 2 = 50 * √2, then AC = 20 * √2.
AL = LC = (1/2) * AC = 10 * √2.
By the Pythagorean theorem, AB² = BL² + AL² = 5² + (10 * √2) ² = 225,
AB = 15.
By the condition AB = BC = 15.
Answer: BC = 15 units.
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.
