Question

AB + BC = 9cm AC + BC = 13cm AB + AC + BC = 14cm AB = ? AC = ? BC = ?

Answer 1

Т.к. АВ + ВС = 13 см, а АВ + ВС + АС = 14 см, по условию ⇒ АС = 1 см.

АВ + ВС = 9 см и АС + ВС = 13 см ⇒ разница АВ и АС = 13 - 9 = 4 см.

Но так как АС = 1 см ⇒ АВ = 1 + 4 = 5 см.

Итак, мы знаем, чему равно АВ и АС.

АВ + АС + ВС = 14 см ⇒ ВС = 14 - АВ - АС = 14 - 5 - 1 = 8 см.

Ответ: ВС = 8 см; АВ = 5 см; АС = 1 см.

Answer 2

To solve this system of equations, let's assign variables to the unknown values:

Let AB be x cm. Let AC be y cm. Let BC be z cm.

From the given equations, we have:

Equation 1: AB + BC = 9 cm Equation 2: AC + BC = 13 cm Equation 3: AB + AC + BC = 14 cm

Now, we can solve the system of equations.

Adding Equation 1 and Equation 2 gives:

(AB + BC) + (AC + BC) = 9 + 13 AB + AC + 2BC = 22 (Equation 4)

Substituting Equation 3 into Equation 4:

14 + 2BC = 22 2BC = 22 - 14 2BC = 8 BC = 4 cm

Substituting the value of BC back into Equation 1:

AB + 4 = 9 AB = 9 - 4 AB = 5 cm

Substituting the value of BC back into Equation 2:

AC + 4 = 13 AC = 13 - 4 AC = 9 cm

Therefore, the solution to the system of equations is: AB = 5 cm AC = 9 cm BC = 4 cm