Question

Помогите решить две задачи. 1. Дано: треугольник ABC, AB-AC=3дм, P=18.12дм, Найти: АС,АВ,ВС. 2. Дано: треугольник АВС, угол А= угол С, АС÷АВ= 3÷4, Р=5.5м, Найти: АС,АВ,ВС. Задачи 7 класс, желательно полное решение. Благодарю заранее♡

Answer 1

Задача 1.
пусть АВ - х, тогда АС - х-30 см, зная что P = 192 см составим и решим уравнение.
х+х-30+х = 192
переносим известное к известному, неизвестное к неизвестному
3х = 222
х = 222:3
х = 74
АВ = 74 см, ВС = 74 см, тогда АС = 74-30 = 44 см.

Answer 2

Problem 1: Finding the lengths of sides in triangle ABC

Given: - Triangle ABC - AB - AC = 3 dm - Perimeter (P) = 18.12 dm

To find: - Lengths of sides AC, AB, and BC

Solution: Let's assume that AB = x dm and AC = (x - 3) dm.

The perimeter of a triangle is the sum of the lengths of its sides. In this case, we have: AB + AC + BC = P

Substituting the values we know: x + (x - 3) + BC = 18.12

Simplifying the equation: 2x - 3 + BC = 18.12 2x + BC = 21.12 BC = 21.12 - 2x

Now, we can use the fact that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. In this case, we have: AB + AC > BC x + (x - 3) > BC 2x - 3 > BC

Substituting the value of BC: 2x - 3 > 21.12 - 2x 4x > 24.12 x > 6.03

Therefore, AB > 6.03 dm.

Now, let's find the lengths of AC and BC using the given information: AC = (x - 3) dm AC = (6.03 - 3) dm AC = 3.03 dm

BC = 21.12 - 2x BC = 21.12 - 2(6.03) BC = 21.12 - 12.06 BC = 9.06 dm

So, the lengths of the sides are: AC = 3.03 dm AB = 6.03 dm BC = 9.06 dm

Note: The lengths of the sides are approximate values rounded to two decimal places.

Problem 2: Finding the lengths of sides in triangle ABC

Given: - Triangle ABC - Angle A = Angle C - AC / AB = 3 / 4 - Perimeter (P) = 5.5 m

To find: - Lengths of sides AC, AB, and BC

Solution: Let's assume that AC = 3x m and AB = 4x m.

The perimeter of a triangle is the sum of the lengths of its sides. In this case, we have: AC + AB + BC = P

Substituting the values we know: 3x + 4x + BC = 5.5

Simplifying the equation: 7x + BC = 5.5 BC = 5.5 - 7x

Now, we can use the fact that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. In this case, we have: AC + AB > BC 3x + 4x > BC 7x > BC

Substituting the value of BC: 7x > 5.5 - 7x 14x > 5.5 x > 0.39

Therefore, AB > 0.39 m.

Now, let's find the lengths of AC and BC using the given information: AC = 3x m AC = 3(0.39) m AC = 1.17 m

BC = 5.5 - 7x BC = 5.5 - 7(0.39) BC = 5.5 - 2.73 BC = 2.77 m

So, the lengths of the sides are: AC = 1.17 m AB = 0.39 m BC = 2.77 m

Note: The lengths of the sides are approximate values rounded to two decimal places.