Question

Запишите выражение для периметра треугольника АВС, если АВ = а см, АС в 2 раза больше, а ВС на 15 см меньше АВ. Составить уравнение и найти стороны треугольника АВС, зная, что его периметр = 95 см?

Answer 1

АВ = аАС = 2аВС = а+15
а + (а+15) + 2а = 954а = 95-154а = 80а=20 см  это АВАС=40 смВС=35 см

Answer 2

Perimeter of Triangle ABC

To find the expression for the perimeter of triangle ABC, we need to determine the lengths of the sides AB, AC, and BC.

Let's denote the length of AB as 'a' cm. According to the given information, AC is twice the length of AB, and BC is 15 cm less than AB.

Therefore, we can express the lengths of the sides as follows: AB = a cm AC = 2a cm BC = (a - 15) cm

The perimeter of a triangle is the sum of the lengths of its sides. So, the expression for the perimeter of triangle ABC is: Perimeter = AB + AC + BC

Substituting the values we found earlier, we get: Perimeter = a cm + 2a cm + (a - 15) cm

Simplifying the expression, we have: Perimeter = 4a - 15 cm

Solving for the Sides of Triangle ABC

Given that the perimeter of triangle ABC is 95 cm, we can set up an equation using the expression for the perimeter and solve for 'a'.

Perimeter = 4a - 15 cm 95 cm = 4a - 15 cm

Adding 15 cm to both sides of the equation, we get: 110 cm = 4a

Dividing both sides of the equation by 4, we find: a = 27.5 cm

Now that we have the value of 'a', we can substitute it back into the expressions for the sides of the triangle to find their lengths.

AB = a cm = 27.5 cm AC = 2a cm = 2 * 27.5 cm = 55 cm BC = (a - 15) cm = 27.5 cm - 15 cm = 12.5 cm

Therefore, the lengths of the sides of triangle ABC are: AB = 27.5 cm AC = 55 cm BC = 12.5 cm

Conclusion

The expression for the perimeter of triangle ABC is 4a - 15 cm. By solving the equation 4a - 15 = 95, we find that the lengths of the sides of triangle ABC are AB = 27.5 cm, AC = 55 cm, and BC = 12.5 cm.