Question

Знайди довжини сторін трикутника АВС ,якщо відомо, що АВ так відноситься до ВС ,як 3 до 2 ,ВС так відноситься до АС ,як 5 до 4 ,а його периметр дорівнює 49,5 м.

Answer 1

Пусть дан треугольник АВС, тогда АВ=3х, ВС=2х=5у, АС=4у. Составим систему: 
$\left \{ {{3x+4y+5y=49.5} \atop {2x=5y}} \right.$
$\left \{ {{ \frac{3*5y}{2}+4y+5y=49.5 } \atop {x= \frac{5y}{2} }} \right.$
$\left \{ {{15y+8y+10y=99} \atop {x= \frac{5y}{2}}} \right.$
$\left \{ {{y=3} \atop {x=7.5}} \right.$.
Тогда АВ=3*7.5=22.5, АС=4*3=12, ВС=3*5=15 см.

Ответ: 22.5, 12 и 15 см.

Answer 2

Finding the Lengths of the Sides of Triangle ABC

To find the lengths of the sides of triangle ABC, we are given the following information:

- AB is to BC as 3 is to 2. - BC is to AC as 5 is to 4. - The perimeter of the triangle is 49.5 meters.

Let's calculate the lengths of the sides of triangle ABC step by step.

1. Let's assume that AB is represented by 3x and BC is represented by 2x, where x is a constant. - AB = 3x - BC = 2x

2. We can use the given information about the ratio of BC to AC to find the length of AC. - BC is to AC as 5 is to 4. - BC/AC = 5/4 - (2x)/AC = 5/4 - Cross-multiplying, we get: 4(2x) = 5(AC) 8x = 5AC AC = (8x)/5

3. The perimeter of the triangle is the sum of the lengths of its sides. - Perimeter = AB + BC + AC - Substituting the values we found: 49.5 = 3x + 2x + (8x)/5

4. Solving the equation for x: - Combining like terms: 49.5 = (15x + 10x + 8x)/5 49.5 = 33x/5 - Cross-multiplying: 5(49.5) = 33x 247.5 = 33x - Dividing both sides by 33: x = 7.5

5. Now that we have the value of x, we can find the lengths of the sides of triangle ABC. - AB = 3x = 3(7.5) = 22.5 meters - BC = 2x = 2(7.5) = 15 meters - AC = (8x)/5 = (8(7.5))/5 = 12 meters

Therefore, the lengths of the sides of triangle ABC are: - AB = 22.5 meters - BC = 15 meters - AC = 12 meters.

Please let me know if there's anything else I can help you with!