If one of the sides of the triangle is 3 cm less than the other, the height divides the third side into segments
June 17, 2021 | education
| If one of the sides of the triangle is 3 cm less than the other, the height divides the third side into segments of 5 cm and 10 cm, then the perimeter of the triangle is ..
We take for x one of the sides of the triangle, then:
x + 3 is the other side;
√ (x ^ 2 – 5 ^ 2) – height;
√ ((x + 3) ^ 2 – 8 ^ 2) – also height.
We get the equation:
x ^ 2 – 25 = (x + 3) ^ 2 – 64;
x ^ 2 – x ^ 2 – 6x – 9 = -64 + 25;
6x + 9 = 39;
x = 5.
Then the second side is equal to:
5 + 3 = 8 cm.
And the third:
5 + 8 = 13.
The perimeter is:
5 + 8 + 13 = 26 cm.
Answer: the desired perimeter of a given triangle is 26 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.