Question

Сумма каких-то двух сторон прямоугольника равна `14`, а сумма каких-то трёх его сторон равна `19`. Какие значения может принимать периметр прямоугольника?

Answer 1

Ответ:

Периметр может быть 28 или 24.

Объяснение:

• Противоположные стороны прямоугольника равны.

Если сумма трех сторон прямоугольника равна 19, а сумма двух сторон  равна 14, то разность этих чисел - длина одной из сторон прямоугольника.

AB = CD = 19 - 14 = 5

Понятно, что сумма этих двух сторон не равна 14.

Тогда, возможно, AB + BC = 14:

BC = 14 - 5 = 9

AD = BC = 9

P = (AB + AD) · 2 = (5 + 9) · 2 = 14 · 2 = 28

Но, возможно, BC + AD = 14, тогда

BC = AD = 14 : 2 = 7

P = (AB + AD) · 2 = (5 + 7) · 2 = 12 · 2 = 24

Answer 2

Perimeter of a Rectangle with Given Side Sums

To find the possible values for the perimeter of a rectangle, given that the sum of two sides is 14 and the sum of three sides is 19, we can use algebraic equations.

Let's assume the length of the rectangle is L and the width is W.

According to the given information, we have two equations:

1. The sum of two sides is 14: L + W = 14. 2. The sum of three sides is 19: 2L + W = 19.

To find the possible values for the perimeter, we need to solve these equations simultaneously.

Solving the Equations

We can solve the equations using substitution or elimination. Let's use the elimination method:

1. Multiply the first equation by 2: 2L + 2W = 28. 2. Subtract the second equation from the first: (2L + 2W) - (2L + W) = 28 - 19. This simplifies to: W = 9.

Now that we have the value of W, we can substitute it back into either of the original equations to find the value of L:

Substituting W = 9 into the first equation: L + 9 = 14. This simplifies to: L = 5.

Therefore, the length of the rectangle is 5 and the width is 9.

Calculating the Perimeter

The perimeter of a rectangle is given by the formula: Perimeter = 2L + 2W.

Substituting the values we found, we get: Perimeter = 2(5) + 2(9) = 10 + 18 = 28.

Therefore, the possible value for the perimeter of the rectangle is 28.

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