Предмет: Математика, автор: kskskfk

Варя и Капа получили по одинаковому прямоугольному листу. Каждая разрезала его на два меньших прямоугольника. У Вариных прямоугольников периметры равны 19 см каждый. У Капиных — 26 см каждый. Какой был периметр у исходного листа?

khatimatmalachieva: можешь мне тоже решение написать?

Ответы

Автор ответа: fearlessforever

0

Ответ:

90 см.

Пошаговое объяснение: Решение: Прямоугольный лист можно разделить на 2 равные части, разрезав вдоль или поперёк. Если назвать стороны прямоугольного листа "а" и "b", то периметр большого листа можно представить через периметры его частей двумя способами.

Пусть Р - периметр большого листа, Р1 - периметр части листа, разрезанного поперёк, Р2 - периметр части листа, разрезанного вдоль.

Р = 2*Р1-2*b

P = 2*P2-2*a

Сложим эти два уравнения:

2*Р = 2*Р1+2*Р2-2*(а+b).

Т.к. 2*(а+b)=Р, то уравнение принимает такой вид:

Р=2*Р1+2*Р2= 2*19+2*26=90 см.

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